Add synthetic array (waveform) DSP support + UX improvements

Adds full array/waveform support through the synthetic DSP engine: a
dsp.Sample value model (scalar or []float64), array ops (index, slice,
sum, mean, min, max, length, fft) with an in-tree radix-2 FFT, and static
type propagation (OpOutputType) that the editor mirrors to colour wires by
data type and flag invalid wirings. Stateful filters and lua stay
scalar-only. Adds a waveform plot mode (x-vs-index trace).

Also: errored-node hover reasons, S/N add-signal/add-node HUD shortcuts in
the synthetic editor, and view-mode widgets that blend with the canvas
background (chrome kept in edit mode).

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

internal/datasource/synthetic/array_graph_test.go

@@ -0,0 +1,222 @@
+package synthetic
+
+import (
+	"context"
+	"log/slog"
+	"math"
+	"os"
+	"testing"
+	"time"
+
+	"github.com/uopi/uopi/internal/broker"
+	"github.com/uopi/uopi/internal/datasource"
+	"github.com/uopi/uopi/internal/dsp"
+)
+
+// evalSampleDef compiles a SignalDef and evaluates it against per-source
+// Samples keyed by source node id, returning the output Sample.
+func evalSampleDef(t *testing.T, def SignalDef, srcVals map[string]dsp.Sample) dsp.Sample {
+	t.Helper()
+	rg, err := compileGraph(def)
+	if err != nil {
+		t.Fatalf("compileGraph: %v", err)
+	}
+	out, err := rg.evalSample(srcVals)
+	if err != nil {
+		t.Fatalf("evalSample: %v", err)
+	}
+	return out
+}
+
+// TestArrayElementwiseChain runs an array source through an elementwise op
+// (gain) and asserts the output stays an array, broadcast per element.
+func TestArrayElementwiseChain(t *testing.T) {
+	def := SignalDef{
+		Name: "scaled",
+		Graph: &Graph{
+			Output: "out",
+			Nodes: []GraphNode{
+				{ID: "a", Kind: "source", DS: "x", Signal: "wave"},
+				{ID: "g", Kind: "op", Op: "gain", Inputs: []string{"a"}, Params: map[string]any{"gain": 2.0}},
+				{ID: "out", Kind: "output", Inputs: []string{"g"}},
+			},
+		},
+	}
+	out := evalSampleDef(t, def, map[string]dsp.Sample{"a": dsp.Array([]float64{1, 2, 3})})
+	if !out.IsArray {
+		t.Fatalf("want array output, got %v", out)
+	}
+	want := []float64{2, 4, 6}
+	for i, v := range want {
+		if out.Arr[i] != v {
+			t.Errorf("scaled[%d]: want %v, got %v", i, v, out.Arr[i])
+		}
+	}
+}
+
+// TestArrayReductionToScalar runs an array source into mean (array→scalar) and
+// asserts a scalar output and an array-output compile type for the producer.
+func TestArrayReductionToScalar(t *testing.T) {
+	def := SignalDef{
+		Name: "avg",
+		Graph: &Graph{
+			Output: "out",
+			Nodes: []GraphNode{
+				{ID: "a", Kind: "source", DS: "x", Signal: "wave"},
+				{ID: "m", Kind: "op", Op: "mean", Inputs: []string{"a"}},
+				{ID: "out", Kind: "output", Inputs: []string{"m"}},
+			},
+		},
+	}
+	out := evalSampleDef(t, def, map[string]dsp.Sample{"a": dsp.Array([]float64{2, 4, 6, 8})})
+	if out.IsArray {
+		t.Fatalf("want scalar output, got array %v", out.Arr)
+	}
+	if math.Abs(out.F-5) > 1e-9 {
+		t.Errorf("mean: want 5, got %v", out.F)
+	}
+}
+
+// TestArrayOutTypeMetadata verifies compileGraph reports an array output type
+// for a pure-elementwise array graph and scalar for a reduction graph.
+func TestArrayOutTypeMetadata(t *testing.T) {
+	arrayGraph := SignalDef{
+		Name: "fftout",
+		Graph: &Graph{
+			Output: "out",
+			Nodes: []GraphNode{
+				{ID: "a", Kind: "source", DS: "x", Signal: "wave"},
+				{ID: "f", Kind: "op", Op: "fft", Inputs: []string{"a"}},
+				{ID: "out", Kind: "output", Inputs: []string{"f"}},
+			},
+		},
+	}
+	rg, err := compileGraph(arrayGraph)
+	if err != nil {
+		t.Fatalf("compileGraph: %v", err)
+	}
+	if rg.outType != dsp.ValArray {
+		t.Errorf("fft graph outType: want ValArray, got %v", rg.outType)
+	}
+
+	reduction := SignalDef{
+		Name: "sumout",
+		Graph: &Graph{
+			Output: "out",
+			Nodes: []GraphNode{
+				{ID: "a", Kind: "source", DS: "x", Signal: "wave"},
+				{ID: "s", Kind: "op", Op: "sum", Inputs: []string{"a"}},
+				{ID: "out", Kind: "output", Inputs: []string{"s"}},
+			},
+		},
+	}
+	rg2, err := compileGraph(reduction)
+	if err != nil {
+		t.Fatalf("compileGraph: %v", err)
+	}
+	if rg2.outType != dsp.ValScalar {
+		t.Errorf("sum graph outType: want ValScalar, got %v", rg2.outType)
+	}
+}
+
+// TestStatefulRejectsArray verifies a stateful op (moving_average) errors when
+// fed an array input at runtime.
+func TestStatefulRejectsArray(t *testing.T) {
+	def := SignalDef{
+		Name: "ma",
+		Graph: &Graph{
+			Output: "out",
+			Nodes: []GraphNode{
+				{ID: "a", Kind: "source", DS: "x", Signal: "wave"},
+				{ID: "m", Kind: "op", Op: "moving_average", Inputs: []string{"a"}, Params: map[string]any{"window": 3.0}},
+				{ID: "out", Kind: "output", Inputs: []string{"m"}},
+			},
+		},
+	}
+	rg, err := compileGraph(def)
+	if err != nil {
+		t.Fatalf("compileGraph: %v", err)
+	}
+	if _, err := rg.evalSample(map[string]dsp.Sample{"a": dsp.Array([]float64{1, 2, 3})}); err == nil {
+		t.Error("expected moving_average to reject an array input")
+	}
+}
+
+// TestSubscribeArrayPassthrough is an end-to-end check that a synthetic with an
+// array-valued source and an elementwise op emits a []float64 over the broker,
+// and that GetMetadata reports the waveform type.
+func TestSubscribeArrayPassthrough(t *testing.T) {
+	log := slog.New(slog.NewTextHandler(os.Stderr, nil))
+	ctx, cancel := context.WithCancel(context.Background())
+	defer cancel()
+
+	base := time.Date(2026, 6, 19, 10, 0, 0, 0, time.UTC)
+	src := &seqSource{name: "src", seq: []datasource.Value{
+		{Timestamp: base.Add(1 * time.Second), Data: []float64{1, 2, 3}, Quality: datasource.QualityGood},
+		{Timestamp: base.Add(2 * time.Second), Data: []float64{4, 5, 6}, Quality: datasource.QualityGood},
+	}}
+
+	brk := broker.New(ctx, log)
+	brk.Register(src)
+	syn := New(t.TempDir(), brk, log)
+	if err := syn.Connect(ctx); err != nil {
+		t.Fatal(err)
+	}
+	// gain x2 elementwise keeps the value an array.
+	if err := syn.AddSignal(SignalDef{
+		Name: "scaled",
+		Graph: &Graph{Output: "out", Nodes: []GraphNode{
+			{ID: "a", Kind: "source", DS: "src", Signal: "x"},
+			{ID: "g", Kind: "op", Op: "gain", Inputs: []string{"a"}, Params: map[string]any{"gain": 2.0}},
+			{ID: "out", Kind: "output", Inputs: []string{"g"}},
+		}},
+	}); err != nil {
+		t.Fatal(err)
+	}
+	// An fft-based signal has a statically-known array output type (the source's
+	// runtime type need not be known), so its metadata reports the waveform type.
+	if err := syn.AddSignal(SignalDef{
+		Name: "spectrum",
+		Graph: &Graph{Output: "out", Nodes: []GraphNode{
+			{ID: "a", Kind: "source", DS: "src", Signal: "x"},
+			{ID: "f", Kind: "op", Op: "fft", Inputs: []string{"a"}},
+			{ID: "out", Kind: "output", Inputs: []string{"f"}},
+		}},
+	}); err != nil {
+		t.Fatal(err)
+	}
+
+	meta, err := syn.GetMetadata(ctx, "spectrum")
+	if err != nil {
+		t.Fatal(err)
+	}
+	if meta.Type != datasource.TypeFloat64Array {
+		t.Errorf("metadata type: want TypeFloat64Array, got %v", meta.Type)
+	}
+
+	ch := make(chan datasource.Value, 8)
+	if _, err := syn.Subscribe(ctx, "scaled", ch); err != nil {
+		t.Fatal(err)
+	}
+
+	want := [][]float64{{2, 4, 6}, {8, 10, 12}}
+	for i, w := range want {
+		select {
+		case v := <-ch:
+			arr, ok := v.Data.([]float64)
+			if !ok {
+				t.Fatalf("emit #%d: want []float64, got %T", i, v.Data)
+			}
+			if len(arr) != len(w) {
+				t.Fatalf("emit #%d: want len %d, got %d", i, len(w), len(arr))
+			}
+			for k, val := range w {
+				if arr[k] != val {
+					t.Errorf("emit #%d [%d]: want %v, got %v", i, k, val, arr[k])
+				}
+			}
+		case <-time.After(2 * time.Second):
+			t.Fatalf("timeout waiting for emit #%d", i)
+		}
+	}
+}

internal/datasource/synthetic/dsp_bridge.go

@@ -126,6 +126,30 @@ func buildNode(d NodeDef) (dsp.Node, error) {
 	case "lua":
 		return &dsp.LuaNode{Script: stringParam(p, "script"), Vars: stringSliceParam(p, "vars")}, nil
 
+	case "index":
+		return &dsp.IndexNode{I: int(floatParam(p, "i"))}, nil
+
+	case "slice":
+		return &dsp.SliceNode{Start: int(floatParam(p, "start")), End: int(floatParam(p, "end"))}, nil
+
+	case "sum":
+		return &dsp.SumNode{}, nil
+
+	case "mean":
+		return &dsp.MeanNode{}, nil
+
+	case "min":
+		return &dsp.MinNode{}, nil
+
+	case "max":
+		return &dsp.MaxNode{}, nil
+
+	case "length":
+		return &dsp.LengthNode{}, nil
+
+	case "fft":
+		return &dsp.FFTNode{}, nil
+
 	default:
 		return nil, fmt.Errorf("unknown node type %q", d.Type)
 	}

internal/datasource/synthetic/graph.go

@@ -13,9 +13,10 @@ import (
 // each node's inputs already resolved. Op-node state maps persist across
 // evaluations (for stateful nodes like moving_average / lua).
 type runtimeGraph struct {
-	order    []*rtNode  // topological order (sources first, output last)
-	sources  []rtSource // source nodes, in topological order
-	outputID string     // id of the output node
+	order    []*rtNode    // topological order (sources first, output last)
+	sources  []rtSource   // source nodes, in topological order
+	outputID string       // id of the output node
+	outType  dsp.ValType  // best-effort output type (scalar/array/unknown)
 }
 
 type rtNode struct {
@@ -41,24 +42,30 @@ func (rg *runtimeGraph) sourceRefs() []broker.SignalRef {
 	return refs
 }
 
-// eval computes the output value given the latest value for each source node
-// (keyed by source node id). Nodes are visited in topological order so every
-// input is already present in vals by the time a node is processed.
-func (rg *runtimeGraph) eval(sourceVals map[string]float64) (float64, error) {
-	vals := make(map[string]float64, len(rg.order))
+// evalSample computes the output Sample (scalar or array) given the latest
+// value for each source node (keyed by source node id). Nodes are visited in
+// topological order so every input is present by the time a node is processed.
+//
+// Op dispatch:
+//   - ArrayNode ops (reductions/producers) run natively on Samples.
+//   - stateless elementwise ops broadcast over array inputs.
+//   - stateful ops (filters) and lua are scalar-only; an array input errors,
+//     since their per-evaluation state cannot be split across array lanes.
+func (rg *runtimeGraph) evalSample(sourceVals map[string]dsp.Sample) (dsp.Sample, error) {
+	vals := make(map[string]dsp.Sample, len(rg.order))
 	for id, v := range sourceVals {
 		vals[id] = v
 	}
 	for _, n := range rg.order {
 		switch n.kind {
 		case "op":
-			in := make([]float64, len(n.inputs))
+			in := make([]dsp.Sample, len(n.inputs))
 			for i, id := range n.inputs {
 				in[i] = vals[id]
 			}
-			r, err := n.op.Process(in, n.state)
+			r, err := evalOp(n, in)
 			if err != nil {
-				return 0, fmt.Errorf("node %s (%s): %w", n.id, n.op.Type(), err)
+				return dsp.Sample{}, fmt.Errorf("node %s (%s): %w", n.id, n.op.Type(), err)
 			}
 			vals[n.id] = r
 		case "output":
@@ -70,6 +77,44 @@ func (rg *runtimeGraph) eval(sourceVals map[string]float64) (float64, error) {
 	return vals[rg.outputID], nil
 }
 
+// evalOp runs a single op node over its Sample inputs, choosing the right
+// execution path for the node type.
+func evalOp(n *rtNode, in []dsp.Sample) (dsp.Sample, error) {
+	if an, ok := n.op.(dsp.ArrayNode); ok {
+		return an.ProcessSample(in, n.state)
+	}
+	if dsp.StatelessElementwise(n.op.Type()) {
+		return dsp.ApplyElementwise(n.op, in, n.state)
+	}
+	// Stateful / lua: scalar-only.
+	row := make([]float64, len(in))
+	for i, s := range in {
+		if s.IsArray {
+			return dsp.Sample{}, fmt.Errorf("does not accept an array input")
+		}
+		row[i] = s.F
+	}
+	r, err := n.op.Process(row, n.state)
+	if err != nil {
+		return dsp.Sample{}, err
+	}
+	return dsp.Scalar(r), nil
+}
+
+// eval is the scalar wrapper around evalSample, kept so callers and tests that
+// deal purely in float64 (legacy linear graphs, scalar sources) are unchanged.
+func (rg *runtimeGraph) eval(sourceVals map[string]float64) (float64, error) {
+	sv := make(map[string]dsp.Sample, len(sourceVals))
+	for id, v := range sourceVals {
+		sv[id] = dsp.Scalar(v)
+	}
+	out, err := rg.evalSample(sv)
+	if err != nil {
+		return 0, err
+	}
+	return out.F, nil
+}
+
 // compileGraph converts a SignalDef into an executable runtimeGraph. When the
 // def carries an explicit Graph it is used directly; otherwise the legacy
 // Inputs+Pipeline form is converted to an equivalent linear graph (see toGraph).
@@ -83,23 +128,42 @@ func compileGraph(def SignalDef) (*runtimeGraph, error) {
 		return nil, err
 	}
 	rg := &runtimeGraph{outputID: g.Output}
+	// nodeType tracks each node's best-effort output type for static
+	// propagation. Sources are unknown at compile time (their real type is
+	// only known once data flows), so type errors here are advisory; runtime
+	// Sample typing is authoritative.
+	nodeType := make(map[string]dsp.ValType, len(order))
 	for _, gn := range order {
 		switch gn.Kind {
 		case "source":
 			rg.sources = append(rg.sources, rtSource{id: gn.ID, ref: broker.SignalRef{DS: gn.DS, Name: gn.Signal}})
+			nodeType[gn.ID] = dsp.ValUnknown
 		case "op":
 			node, err := buildNode(NodeDef{Type: gn.Op, Params: gn.Params})
 			if err != nil {
 				return nil, fmt.Errorf("node %q: %w", gn.ID, err)
 			}
+			inTypes := make([]dsp.ValType, len(gn.Inputs))
+			for i, id := range gn.Inputs {
+				inTypes[i] = nodeType[id]
+			}
+			ot, terr := dsp.OpOutputType(gn.Op, inTypes)
+			if terr != nil {
+				return nil, fmt.Errorf("node %q: %w", gn.ID, terr)
+			}
+			nodeType[gn.ID] = ot
 			rg.order = append(rg.order, &rtNode{id: gn.ID, kind: "op", op: node, state: map[string]any{}, inputs: gn.Inputs})
 		case "output":
 			rg.outputID = gn.ID
+			if len(gn.Inputs) > 0 {
+				nodeType[gn.ID] = nodeType[gn.Inputs[0]]
+			}
 			rg.order = append(rg.order, &rtNode{id: gn.ID, kind: "output", inputs: gn.Inputs})
 		default:
 			return nil, fmt.Errorf("node %q: unknown kind %q", gn.ID, gn.Kind)
 		}
 	}
+	rg.outType = nodeType[rg.outputID]
 	return rg, nil
 }
 

internal/datasource/synthetic/synthetic.go

@@ -13,6 +13,7 @@ import (
 
 	"github.com/uopi/uopi/internal/broker"
 	"github.com/uopi/uopi/internal/datasource"
+	"github.com/uopi/uopi/internal/dsp"
 )
 
 const definitionsFile = "synthetic.json"
@@ -78,7 +79,7 @@ func (s *Synthetic) ListSignals(_ context.Context) ([]datasource.Metadata, error
 
 	out := make([]datasource.Metadata, 0, len(s.signals))
 	for _, st := range s.signals {
-		out = append(out, defToMetadata(st.def))
+		out = append(out, defToMetadata(st.def, outTypeOf(st)))
 	}
 	return out, nil
 }
@@ -93,7 +94,7 @@ func (s *Synthetic) FilteredMetadata(keep func(SignalDef) bool) []datasource.Met
 	out := make([]datasource.Metadata, 0, len(s.signals))
 	for _, st := range s.signals {
 		if keep(st.def) {
-			out = append(out, defToMetadata(st.def))
+			out = append(out, defToMetadata(st.def, outTypeOf(st)))
 		}
 	}
 	return out
@@ -108,7 +109,7 @@ func (s *Synthetic) GetMetadata(_ context.Context, signal string) (datasource.Me
 	if !ok {
 		return datasource.Metadata{}, datasource.ErrNotFound
 	}
-	return defToMetadata(st.def), nil
+	return defToMetadata(st.def, outTypeOf(st)), nil
 }
 
 // Subscribe registers ch to receive computed values for the named signal.
@@ -138,7 +139,7 @@ func (s *Synthetic) Subscribe(ctx context.Context, signal string, ch chan<- data
 		defer cancel()
 
 		// Latest value and timestamp per source node id.
-		latest := make(map[string]float64, len(refs))
+		latest := make(map[string]dsp.Sample, len(refs))
 		latestTs := make([]time.Time, len(refs))
 		ready := make([]bool, len(refs))
 
@@ -163,7 +164,7 @@ func (s *Synthetic) Subscribe(ctx context.Context, signal string, ch chan<- data
 							if !ok {
 								return
 							}
-							val := toFloat64(u.Value.Data)
+							val := toSample(u.Value.Data)
 							select {
 							case updateCh <- indexedUpdate{idx: idx, val: val, ts: u.Value.Timestamp}:
 							default:
@@ -224,7 +225,7 @@ func (s *Synthetic) Subscribe(ctx context.Context, signal string, ch chan<- data
 					return
 				}
 
-				result, err := cur.rg.eval(latest)
+				result, err := cur.rg.evalSample(latest)
 				if err != nil {
 					s.log.Warn("synthetic: pipeline error", "signal", signal, "err", err)
 					continue
@@ -232,7 +233,7 @@ func (s *Synthetic) Subscribe(ctx context.Context, signal string, ch chan<- data
 
 				v := datasource.Value{
 					Timestamp: outTs,
-					Data:      result,
+					Data:      result.AsAny(),
 					Quality:   datasource.QualityGood,
 				}
 				select {
@@ -421,11 +422,17 @@ func (s *Synthetic) startSignal(def SignalDef) error {
 	return nil
 }
 
-// defToMetadata converts a SignalDef into a datasource.Metadata.
-func defToMetadata(def SignalDef) datasource.Metadata {
+// defToMetadata converts a SignalDef into a datasource.Metadata. outType is the
+// compiled graph's best-effort output type; an array output is reported as a
+// waveform (TypeFloat64Array) so widgets can pick a compatible view.
+func defToMetadata(def SignalDef, outType dsp.ValType) datasource.Metadata {
+	dt := datasource.TypeFloat64
+	if outType == dsp.ValArray {
+		dt = datasource.TypeFloat64Array
+	}
 	return datasource.Metadata{
 		Name:        def.Name,
-		Type:        datasource.TypeFloat64,
+		Type:        dt,
 		Unit:        def.Meta.Unit,
 		Description: def.Meta.Description,
 		DisplayLow:  def.Meta.DisplayLow,
@@ -434,7 +441,38 @@ func defToMetadata(def SignalDef) datasource.Metadata {
 	}
 }
 
-// toFloat64 coerces any numeric value from a datasource.Value.Data to float64.
+// outTypeOf returns the compiled output type for a signal state, or unknown.
+func outTypeOf(st *signalState) dsp.ValType {
+	if st == nil || st.rg == nil {
+		return dsp.ValUnknown
+	}
+	return st.rg.outType
+}
+
+// toSample coerces a datasource.Value.Data into a dsp.Sample: arrays become
+// array Samples (waveforms), everything else a scalar Sample.
+func toSample(v any) dsp.Sample {
+	switch val := v.(type) {
+	case []float64:
+		return dsp.Array(val)
+	case []float32:
+		out := make([]float64, len(val))
+		for i, e := range val {
+			out[i] = float64(e)
+		}
+		return dsp.Array(out)
+	case []int:
+		out := make([]float64, len(val))
+		for i, e := range val {
+			out[i] = float64(e)
+		}
+		return dsp.Array(out)
+	default:
+		return dsp.Scalar(toFloat64(v))
+	}
+}
+
+// toFloat64 coerces any numeric scalar value from a datasource.Value.Data to float64.
 func toFloat64(v any) float64 {
 	switch val := v.(type) {
 	case float64:
@@ -460,6 +498,6 @@ func toFloat64(v any) float64 {
 // indexedUpdate carries a value from one upstream goroutine to the pipeline runner.
 type indexedUpdate struct {
 	idx int
-	val float64
+	val dsp.Sample
 	ts  time.Time
 }

internal/dsp/array_nodes.go

@@ -0,0 +1,230 @@
+package dsp
+
+import (
+	"errors"
+	"fmt"
+	"math"
+)
+
+// This file holds ArrayNode ops: those that operate natively on waveform
+// (float64 array) Samples — reductions (array→scalar), producers (array→array),
+// and element access. Each also implements the legacy scalar Node interface
+// (treating a scalar as a single-element array) so it remains usable from the
+// scalar eval path.
+
+// reductionProcess adapts a scalar Process call to a reduction ArrayNode.
+func reductionProcess(n ArrayNode, in []float64, st map[string]any) (float64, error) {
+	s, err := n.ProcessSample(scalarInputs(in), st)
+	if err != nil {
+		return 0, err
+	}
+	return s.F, nil
+}
+
+// ── IndexNode ───────────────────────────────────────────────────────────────
+
+// IndexNode extracts element I of an array input (array→scalar).
+type IndexNode struct{ I int }
+
+func (n *IndexNode) Type() string { return "index" }
+func (n *IndexNode) Process(in []float64, st map[string]any) (float64, error) {
+	return reductionProcess(n, in, st)
+}
+func (n *IndexNode) ProcessSample(in []Sample, _ map[string]any) (Sample, error) {
+	if len(in) == 0 {
+		return Sample{}, errors.New("index: no inputs")
+	}
+	arr := in[0].AsArray()
+	if n.I < 0 || n.I >= len(arr) {
+		return Sample{}, fmt.Errorf("index: %d out of range [0,%d)", n.I, len(arr))
+	}
+	return Scalar(arr[n.I]), nil
+}
+
+// ── SliceNode ───────────────────────────────────────────────────────────────
+
+// SliceNode returns a sub-range [Start,End) of an array input (array→array),
+// clamped to the array bounds. End <= 0 means "to the end".
+type SliceNode struct{ Start, End int }
+
+func (n *SliceNode) Type() string { return "slice" }
+func (n *SliceNode) Process(in []float64, st map[string]any) (float64, error) {
+	s, err := n.ProcessSample(scalarInputs(in), st)
+	if err != nil {
+		return 0, err
+	}
+	if len(s.Arr) == 0 {
+		return 0, nil
+	}
+	return s.Arr[0], nil
+}
+func (n *SliceNode) ProcessSample(in []Sample, _ map[string]any) (Sample, error) {
+	if len(in) == 0 {
+		return Sample{}, errors.New("slice: no inputs")
+	}
+	arr := in[0].AsArray()
+	start := n.Start
+	if start < 0 {
+		start = 0
+	}
+	if start > len(arr) {
+		start = len(arr)
+	}
+	end := n.End
+	if end <= 0 || end > len(arr) {
+		end = len(arr)
+	}
+	if end < start {
+		end = start
+	}
+	out := make([]float64, end-start)
+	copy(out, arr[start:end])
+	return Array(out), nil
+}
+
+// ── reductions ────────────────────────────────────────────────────────────────
+
+// SumNode sums an array input (array→scalar).
+type SumNode struct{}
+
+func (n *SumNode) Type() string { return "sum" }
+func (n *SumNode) Process(in []float64, st map[string]any) (float64, error) {
+	return reductionProcess(n, in, st)
+}
+func (n *SumNode) ProcessSample(in []Sample, _ map[string]any) (Sample, error) {
+	if len(in) == 0 {
+		return Sample{}, errors.New("sum: no inputs")
+	}
+	var s float64
+	for _, v := range in[0].AsArray() {
+		s += v
+	}
+	return Scalar(s), nil
+}
+
+// MeanNode averages an array input (array→scalar).
+type MeanNode struct{}
+
+func (n *MeanNode) Type() string { return "mean" }
+func (n *MeanNode) Process(in []float64, st map[string]any) (float64, error) {
+	return reductionProcess(n, in, st)
+}
+func (n *MeanNode) ProcessSample(in []Sample, _ map[string]any) (Sample, error) {
+	if len(in) == 0 {
+		return Sample{}, errors.New("mean: no inputs")
+	}
+	arr := in[0].AsArray()
+	if len(arr) == 0 {
+		return Scalar(0), nil
+	}
+	var s float64
+	for _, v := range arr {
+		s += v
+	}
+	return Scalar(s / float64(len(arr))), nil
+}
+
+// MinNode returns the minimum element of an array input (array→scalar).
+type MinNode struct{}
+
+func (n *MinNode) Type() string { return "min" }
+func (n *MinNode) Process(in []float64, st map[string]any) (float64, error) {
+	return reductionProcess(n, in, st)
+}
+func (n *MinNode) ProcessSample(in []Sample, _ map[string]any) (Sample, error) {
+	if len(in) == 0 {
+		return Sample{}, errors.New("min: no inputs")
+	}
+	arr := in[0].AsArray()
+	if len(arr) == 0 {
+		return Scalar(0), nil
+	}
+	m := arr[0]
+	for _, v := range arr[1:] {
+		if v < m {
+			m = v
+		}
+	}
+	return Scalar(m), nil
+}
+
+// MaxNode returns the maximum element of an array input (array→scalar).
+type MaxNode struct{}
+
+func (n *MaxNode) Type() string { return "max" }
+func (n *MaxNode) Process(in []float64, st map[string]any) (float64, error) {
+	return reductionProcess(n, in, st)
+}
+func (n *MaxNode) ProcessSample(in []Sample, _ map[string]any) (Sample, error) {
+	if len(in) == 0 {
+		return Sample{}, errors.New("max: no inputs")
+	}
+	arr := in[0].AsArray()
+	if len(arr) == 0 {
+		return Scalar(0), nil
+	}
+	m := arr[0]
+	for _, v := range arr[1:] {
+		if v > m {
+			m = v
+		}
+	}
+	return Scalar(m), nil
+}
+
+// LengthNode returns the element count of an array input (array→scalar).
+type LengthNode struct{}
+
+func (n *LengthNode) Type() string { return "length" }
+func (n *LengthNode) Process(in []float64, st map[string]any) (float64, error) {
+	return reductionProcess(n, in, st)
+}
+func (n *LengthNode) ProcessSample(in []Sample, _ map[string]any) (Sample, error) {
+	if len(in) == 0 {
+		return Sample{}, errors.New("length: no inputs")
+	}
+	return Scalar(float64(len(in[0].AsArray()))), nil
+}
+
+// ── FFTNode ────────────────────────────────────────────────────────────────
+
+// FFTNode computes the magnitude spectrum of an array input (array→array). The
+// input is zero-padded to the next power of two; the output has that length and
+// holds |X[k]| for each frequency bin.
+type FFTNode struct{}
+
+func (n *FFTNode) Type() string { return "fft" }
+func (n *FFTNode) Process(in []float64, st map[string]any) (float64, error) {
+	s, err := n.ProcessSample(scalarInputs(in), st)
+	if err != nil {
+		return 0, err
+	}
+	if len(s.Arr) == 0 {
+		return 0, nil
+	}
+	return s.Arr[0], nil
+}
+func (n *FFTNode) ProcessSample(in []Sample, _ map[string]any) (Sample, error) {
+	if len(in) == 0 {
+		return Sample{}, errors.New("fft: no inputs")
+	}
+	return Array(fftMagnitude(in[0].AsArray())), nil
+}
+
+// fftMagnitude returns the magnitude spectrum of x, zero-padded to the next
+// power of two. Returns an empty slice for empty input.
+func fftMagnitude(x []float64) []float64 {
+	if len(x) == 0 {
+		return nil
+	}
+	n := nextPow2(len(x))
+	re := make([]float64, n)
+	im := make([]float64, n)
+	copy(re, x)
+	fftRadix2(re, im)
+	mag := make([]float64, n)
+	for i := range mag {
+		mag[i] = math.Hypot(re[i], im[i])
+	}
+	return mag
+}

internal/dsp/array_nodes_test.go

@@ -0,0 +1,213 @@
+package dsp
+
+import (
+	"math"
+	"testing"
+)
+
+func TestSampleRoundTrip(t *testing.T) {
+	s := Scalar(3.5)
+	if s.IsArray {
+		t.Error("Scalar should not be an array")
+	}
+	if s.Type() != ValScalar {
+		t.Errorf("Scalar type: want ValScalar, got %v", s.Type())
+	}
+	if s.AsAny() != 3.5 {
+		t.Errorf("Scalar AsAny: want 3.5, got %v", s.AsAny())
+	}
+	if got := s.AsArray(); len(got) != 1 || got[0] != 3.5 {
+		t.Errorf("Scalar AsArray: want [3.5], got %v", got)
+	}
+
+	a := Array([]float64{1, 2, 3})
+	if !a.IsArray {
+		t.Error("Array should be an array")
+	}
+	if a.Type() != ValArray {
+		t.Errorf("Array type: want ValArray, got %v", a.Type())
+	}
+	got, ok := a.AsAny().([]float64)
+	if !ok || len(got) != 3 {
+		t.Errorf("Array AsAny: want []float64 len 3, got %v", a.AsAny())
+	}
+}
+
+func TestApplyElementwiseAllScalar(t *testing.T) {
+	n := &AddNode{}
+	out, err := ApplyElementwise(n, []Sample{Scalar(2), Scalar(3)}, map[string]any{})
+	if err != nil {
+		t.Fatal(err)
+	}
+	if out.IsArray || out.F != 5 {
+		t.Errorf("all-scalar add: want scalar 5, got %v", out)
+	}
+}
+
+func TestApplyElementwiseBroadcast(t *testing.T) {
+	// array ⊕ scalar: scalar is a constant broadcast across the array.
+	n := &AddNode{}
+	out, err := ApplyElementwise(n, []Sample{Array([]float64{1, 2, 3}), Scalar(10)}, map[string]any{})
+	if err != nil {
+		t.Fatal(err)
+	}
+	if !out.IsArray {
+		t.Fatalf("array+scalar: want array, got %v", out)
+	}
+	want := []float64{11, 12, 13}
+	for i, v := range want {
+		if out.Arr[i] != v {
+			t.Errorf("array+scalar[%d]: want %v, got %v", i, v, out.Arr[i])
+		}
+	}
+}
+
+func TestApplyElementwiseArrayArray(t *testing.T) {
+	n := &MultiplyNode{}
+	out, err := ApplyElementwise(n, []Sample{Array([]float64{1, 2, 3}), Array([]float64{4, 5, 6})}, map[string]any{})
+	if err != nil {
+		t.Fatal(err)
+	}
+	want := []float64{4, 10, 18}
+	for i, v := range want {
+		if out.Arr[i] != v {
+			t.Errorf("array*array[%d]: want %v, got %v", i, v, out.Arr[i])
+		}
+	}
+}
+
+func TestApplyElementwiseLengthMismatch(t *testing.T) {
+	n := &AddNode{}
+	_, err := ApplyElementwise(n, []Sample{Array([]float64{1, 2}), Array([]float64{1, 2, 3})}, map[string]any{})
+	if err == nil {
+		t.Error("expected length-mismatch error")
+	}
+}
+
+func TestReductionNodes(t *testing.T) {
+	arr := []Sample{Array([]float64{2, 4, 6, 8})}
+	cases := []struct {
+		name string
+		node ArrayNode
+		want float64
+	}{
+		{"sum", &SumNode{}, 20},
+		{"mean", &MeanNode{}, 5},
+		{"min", &MinNode{}, 2},
+		{"max", &MaxNode{}, 8},
+		{"length", &LengthNode{}, 4},
+		{"index", &IndexNode{I: 2}, 6},
+	}
+	for _, tc := range cases {
+		t.Run(tc.name, func(t *testing.T) {
+			out, err := tc.node.ProcessSample(arr, map[string]any{})
+			if err != nil {
+				t.Fatal(err)
+			}
+			if out.IsArray || out.F != tc.want {
+				t.Errorf("%s: want scalar %v, got %v", tc.name, tc.want, out)
+			}
+		})
+	}
+}
+
+func TestIndexNodeOutOfRange(t *testing.T) {
+	n := &IndexNode{I: 9}
+	_, err := n.ProcessSample([]Sample{Array([]float64{1, 2, 3})}, map[string]any{})
+	if err == nil {
+		t.Error("expected out-of-range error")
+	}
+}
+
+func TestSliceNode(t *testing.T) {
+	n := &SliceNode{Start: 1, End: 3}
+	out, err := n.ProcessSample([]Sample{Array([]float64{10, 20, 30, 40})}, map[string]any{})
+	if err != nil {
+		t.Fatal(err)
+	}
+	want := []float64{20, 30}
+	if len(out.Arr) != len(want) {
+		t.Fatalf("slice: want len %d, got %d", len(want), len(out.Arr))
+	}
+	for i, v := range want {
+		if out.Arr[i] != v {
+			t.Errorf("slice[%d]: want %v, got %v", i, v, out.Arr[i])
+		}
+	}
+}
+
+func TestFFTMagnitude(t *testing.T) {
+	// A constant signal has all energy in bin 0 (the DC term equals the sum).
+	x := []float64{1, 1, 1, 1}
+	mag := fftMagnitude(x)
+	if len(mag) != 4 {
+		t.Fatalf("fft len: want 4, got %d", len(mag))
+	}
+	if math.Abs(mag[0]-4) > 1e-9 {
+		t.Errorf("fft DC bin: want 4, got %v", mag[0])
+	}
+	for k := 1; k < len(mag); k++ {
+		if math.Abs(mag[k]) > 1e-9 {
+			t.Errorf("fft bin %d: want ~0, got %v", k, mag[k])
+		}
+	}
+}
+
+func TestFFTSingleTone(t *testing.T) {
+	// One full cycle of a cosine over 8 samples → energy in bins 1 and N-1.
+	n := 8
+	x := make([]float64, n)
+	for i := range x {
+		x[i] = math.Cos(2 * math.Pi * float64(i) / float64(n))
+	}
+	mag := fftMagnitude(x)
+	if math.Abs(mag[1]-float64(n)/2) > 1e-6 {
+		t.Errorf("fft tone bin 1: want %v, got %v", float64(n)/2, mag[1])
+	}
+	if math.Abs(mag[n-1]-float64(n)/2) > 1e-6 {
+		t.Errorf("fft tone bin %d: want %v, got %v", n-1, float64(n)/2, mag[n-1])
+	}
+}
+
+func TestOpOutputType(t *testing.T) {
+	cases := []struct {
+		op      string
+		in      []ValType
+		want    ValType
+		wantErr bool
+	}{
+		// reductions → scalar regardless of input
+		{"sum", []ValType{ValArray}, ValScalar, false},
+		{"mean", []ValType{ValScalar}, ValScalar, false},
+		{"index", []ValType{ValUnknown}, ValScalar, false},
+		// array producers require array, yield array
+		{"fft", []ValType{ValArray}, ValArray, false},
+		{"slice", []ValType{ValUnknown}, ValArray, false},
+		{"fft", []ValType{ValScalar}, ValUnknown, true},
+		// scalar-only reject arrays
+		{"moving_average", []ValType{ValScalar}, ValScalar, false},
+		{"lua", []ValType{ValArray}, ValUnknown, true},
+		{"rms", []ValType{ValUnknown}, ValScalar, false},
+		// elementwise: array if any array, scalar if all scalar, else unknown
+		{"add", []ValType{ValScalar, ValScalar}, ValScalar, false},
+		{"add", []ValType{ValArray, ValScalar}, ValArray, false},
+		{"gain", []ValType{ValUnknown}, ValUnknown, false},
+		{"expr", []ValType{ValArray, ValScalar}, ValArray, false},
+	}
+	for _, tc := range cases {
+		got, err := OpOutputType(tc.op, tc.in)
+		if tc.wantErr {
+			if err == nil {
+				t.Errorf("OpOutputType(%q,%v): expected error", tc.op, tc.in)
+			}
+			continue
+		}
+		if err != nil {
+			t.Errorf("OpOutputType(%q,%v): unexpected error %v", tc.op, tc.in, err)
+			continue
+		}
+		if got != tc.want {
+			t.Errorf("OpOutputType(%q,%v): want %v, got %v", tc.op, tc.in, tc.want, got)
+		}
+	}
+}

internal/dsp/fft.go

@@ -0,0 +1,58 @@
+package dsp
+
+import "math"
+
+// nextPow2 returns the smallest power of two >= n (and at least 1).
+func nextPow2(n int) int {
+	p := 1
+	for p < n {
+		p <<= 1
+	}
+	return p
+}
+
+// fftRadix2 computes the in-place iterative radix-2 Cooley-Tukey FFT of the
+// complex signal held in re/im. len(re) == len(im) must be a power of two. The
+// transform overwrites re/im with the frequency-domain result. This is a small
+// self-contained implementation (no external dependency) used by the synthetic
+// fft op.
+func fftRadix2(re, im []float64) {
+	n := len(re)
+	if n <= 1 {
+		return
+	}
+
+	// Bit-reversal permutation.
+	for i, j := 1, 0; i < n; i++ {
+		bit := n >> 1
+		for ; j&bit != 0; bit >>= 1 {
+			j ^= bit
+		}
+		j ^= bit
+		if i < j {
+			re[i], re[j] = re[j], re[i]
+			im[i], im[j] = im[j], im[i]
+		}
+	}
+
+	// Danielson-Lanczos butterflies.
+	for length := 2; length <= n; length <<= 1 {
+		ang := -2 * math.Pi / float64(length)
+		wReal, wImag := math.Cos(ang), math.Sin(ang)
+		for i := 0; i < n; i += length {
+			curReal, curImag := 1.0, 0.0
+			half := length >> 1
+			for k := 0; k < half; k++ {
+				a := i + k
+				b := i + k + half
+				tReal := curReal*re[b] - curImag*im[b]
+				tImag := curReal*im[b] + curImag*re[b]
+				re[b] = re[a] - tReal
+				im[b] = im[a] - tImag
+				re[a] += tReal
+				im[a] += tImag
+				curReal, curImag = curReal*wReal-curImag*wImag, curReal*wImag+curImag*wReal
+			}
+		}
+	}
+}

internal/dsp/sample.go

@@ -0,0 +1,151 @@
+package dsp
+
+import "fmt"
+
+// ValType is the data type of a Sample: a scalar float, a float array
+// (waveform), or — at graph-compile time, before a source's real type is
+// known — unknown.
+type ValType uint8
+
+const (
+	ValUnknown ValType = iota
+	ValScalar
+	ValArray
+)
+
+func (t ValType) String() string {
+	switch t {
+	case ValScalar:
+		return "scalar"
+	case ValArray:
+		return "array"
+	default:
+		return "unknown"
+	}
+}
+
+// Sample is a value flowing through the synthetic DSP graph: either a scalar
+// float64 or a float64 array (waveform). It is the array-aware counterpart of
+// the bare float64 the legacy scalar Node interface uses.
+type Sample struct {
+	F       float64
+	Arr     []float64
+	IsArray bool
+}
+
+// Scalar wraps a float64 as a scalar Sample.
+func Scalar(f float64) Sample { return Sample{F: f} }
+
+// Array wraps a []float64 as an array Sample.
+func Array(a []float64) Sample { return Sample{Arr: a, IsArray: true} }
+
+// Type reports whether the sample is a scalar or an array.
+func (s Sample) Type() ValType {
+	if s.IsArray {
+		return ValArray
+	}
+	return ValScalar
+}
+
+// AsAny returns the value in the form datasource.Value.Data expects: a
+// []float64 for arrays, a float64 for scalars.
+func (s Sample) AsAny() any {
+	if s.IsArray {
+		return s.Arr
+	}
+	return s.F
+}
+
+// AsArray returns the sample's data as a slice: the array itself, or a
+// single-element slice for a scalar. Used by reductions that accept either.
+func (s Sample) AsArray() []float64 {
+	if s.IsArray {
+		return s.Arr
+	}
+	return []float64{s.F}
+}
+
+// ArrayNode is an optional extension of Node implemented by ops that operate
+// natively on Samples (reductions array→scalar, producers array→array, etc.).
+// eval prefers ProcessSample when a node implements it.
+type ArrayNode interface {
+	Node
+	ProcessSample(inputs []Sample, state map[string]any) (Sample, error)
+}
+
+// statelessElementwise lists scalar ops that are safe to broadcast element-wise
+// over array inputs: they hold no per-evaluation state, so running the legacy
+// Process once per array lane is well-defined. Stateful ops (moving_average,
+// rms, lowpass, derivative, integrate) and lua are excluded — a single shared
+// state map cannot be meaningfully split across lanes.
+var statelessElementwise = map[string]bool{
+	"gain": true, "offset": true, "add": true, "subtract": true,
+	"multiply": true, "divide": true, "clamp": true, "threshold": true,
+	"expr": true,
+}
+
+// StatelessElementwise reports whether a scalar op type may be broadcast over
+// array inputs via ApplyElementwise.
+func StatelessElementwise(nodeType string) bool { return statelessElementwise[nodeType] }
+
+// scalarInputs wraps a legacy float64 input slice as scalar Samples.
+func scalarInputs(in []float64) []Sample {
+	out := make([]Sample, len(in))
+	for i, v := range in {
+		out[i] = Scalar(v)
+	}
+	return out
+}
+
+// ApplyElementwise runs a stateless scalar Node over Sample inputs. If every
+// input is scalar it calls Process once and wraps the result. If any input is
+// an array it broadcasts: scalar inputs act as constants, all array inputs must
+// share a common length (else an error), and Process is invoked once per index.
+//
+// The node MUST be stateless (see StatelessElementwise) — a shared state map
+// cannot be split across array lanes.
+func ApplyElementwise(n Node, inputs []Sample, state map[string]any) (Sample, error) {
+	// Determine the array length, if any input is an array.
+	length := -1
+	for _, s := range inputs {
+		if !s.IsArray {
+			continue
+		}
+		if length == -1 {
+			length = len(s.Arr)
+		} else if len(s.Arr) != length {
+			return Sample{}, fmt.Errorf("%s: array length mismatch (%d vs %d)", n.Type(), length, len(s.Arr))
+		}
+	}
+
+	if length == -1 {
+		// All scalar — single legacy call.
+		row := make([]float64, len(inputs))
+		for i, s := range inputs {
+			row[i] = s.F
+		}
+		r, err := n.Process(row, state)
+		if err != nil {
+			return Sample{}, err
+		}
+		return Scalar(r), nil
+	}
+
+	out := make([]float64, length)
+	row := make([]float64, len(inputs))
+	for i := 0; i < length; i++ {
+		for j, s := range inputs {
+			if s.IsArray {
+				row[j] = s.Arr[i]
+			} else {
+				row[j] = s.F
+			}
+		}
+		r, err := n.Process(row, state)
+		if err != nil {
+			return Sample{}, err
+		}
+		out[i] = r
+	}
+	return Array(out), nil
+}

internal/dsp/types.go

@@ -0,0 +1,74 @@
+package dsp
+
+import "fmt"
+
+// Op type categories for static (compile-time / editor) type propagation.
+// These mirror the runtime dispatch in the synthetic graph evaluator and the
+// frontend's inferNodeTypes (web/src/lib/synthTypes.ts) — keep the three in
+// sync; a parity test guards the Go/TS pair.
+var (
+	// reductionOps collapse an array (or scalar) to a single scalar.
+	reductionOps = map[string]bool{
+		"index": true, "length": true, "sum": true,
+		"mean": true, "min": true, "max": true,
+	}
+	// arrayProducerOps require an array input and yield an array.
+	arrayProducerOps = map[string]bool{
+		"fft": true, "slice": true,
+	}
+	// scalarOnlyOps reject array inputs and yield a scalar. Stateful filters
+	// plus lua (whose state/closure cannot be broadcast per array lane).
+	scalarOnlyOps = map[string]bool{
+		"moving_average": true, "rms": true, "lowpass": true,
+		"derivative": true, "integrate": true, "lua": true,
+	}
+)
+
+// OpOutputType reports the output ValType of an op given its input types, and
+// an error if the inputs are definitely incompatible with the op. Inputs may be
+// ValUnknown (a source whose real type is not yet known at compile time); such
+// inputs never trigger an error — runtime Sample typing is authoritative.
+func OpOutputType(op string, in []ValType) (ValType, error) {
+	switch {
+	case reductionOps[op]:
+		return ValScalar, nil
+
+	case arrayProducerOps[op]:
+		for _, t := range in {
+			if t == ValScalar {
+				return ValUnknown, fmt.Errorf("%s requires an array input", op)
+			}
+		}
+		return ValArray, nil
+
+	case scalarOnlyOps[op]:
+		for _, t := range in {
+			if t == ValArray {
+				return ValUnknown, fmt.Errorf("%s does not accept an array input", op)
+			}
+		}
+		return ValScalar, nil
+
+	default:
+		// Elementwise stateless ops (gain, offset, add, subtract, multiply,
+		// divide, clamp, threshold, expr): array if any input is an array,
+		// scalar if all inputs are definitely scalar, otherwise unknown.
+		anyArray, anyUnknown := false, false
+		for _, t := range in {
+			switch t {
+			case ValArray:
+				anyArray = true
+			case ValUnknown:
+				anyUnknown = true
+			}
+		}
+		switch {
+		case anyArray:
+			return ValArray, nil
+		case anyUnknown:
+			return ValUnknown, nil
+		default:
+			return ValScalar, nil
+		}
+	}
+}