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group_delay

Builtin index · Signal processing

result = group_delay(filt, [n=512])

Input: filt, n · Output: result

What it is

filt: a Model (kind "filter"); n (optional number, default 512).

Overloads

One call shape — this function is not overloaded.

CodeInputOutputDescription
result = group_delay(filt, [n=512])
filt Modelfilt: a Model (kind "filter").
n number, optional (default 512)n (optional number, default 512).
result vector
Returns a length-n real vector, -dφ/dω in samples, same n-point/frequency-axis convention as freqz. For a linear-phase fir1 lowpass this is exactly constant at n_order/2 samples.

Examples

From the documentation, and run by the build -- the output and the figure below are what the engine actually produced. Simplest first.

fs = 1000
ep = ellip(4, 1, 40, "low", 100, fs)
c1 = cheby1(4, 1, "low", 100, fs)
c2 = cheby2(4, 40, "low", 100, fs)
print("ellip stable: {is_stable(ep)}, cheby1 stable: {is_stable(c1)}, cheby2 stable: {is_stable(c2)}")

fir = fir1(6, 100, kind="low", window="hamming", fs=fs)
b = fir.b
a = [1]
n = 0:1:255
t = n / fs
x = sin(2*pi*40*t) + sin(2*pi*300*t)
y  = filter_ba(b, a, x)
y2 = lfilter(b, a, x)               # lfilter is the same builtin under another name

print("filter_ba/lfilter agree: {max(abs(y - y2)) < 1e-12}")

lsq = firls(20, [0, 0.2, 0.3, 1.0], [1, 1, 0, 0])   # low-pass band edges/response

print("firls taps: {length(lsq.b)}")

gd = group_delay(fir, 256)
print("FIR group delay (should be ~order/2=3): {gd[10]}")
print("ellip filter has {length(poles(ep))} poles")

ep.fvtool()   # 2x2 magnitude/phase/group-delay/impulse-response figure

pzplot(ep)    # pole-zero plot with the unit circle and stability verdict
output
ellip stable: true, cheby1 stable: true, cheby2 stable: true
filter_ba/lfilter agree: true
firls taps: 21
FIR group delay (should be ~order/2=3): 3
ellip filter has 4 poles
-80 -60 -40 -20 0 0 150 300 450 Magnitude Response Frequency (Hz) Magnitude (dB) -150 -100 -50 0 50 100 150 0 150 300 450 Phase Response Frequency (Hz) Phase (deg) -250 -200 -150 -100 -50 0 0 150 300 450 Group Delay Frequency (Hz) Delay (samples) -20 -10 0 10 20 0 20 40 60 x=-0.135, y=0.991 x=-0.135, y=-0.991 x=0.57, y=0.821 x=0.57, y=-0.821 Pole-Zero Plot (stable) Real part Imaginary part

from signal-processing

How it works

group_delay(filt, [n=512]) — -dφ/dω in samples, same n points/frequency-axis convention as freqz. For a fir1 lowpass (symmetric/linear-phase by construction) this is exactly constant at n_order/2 samples; computed the same unwrap-then-differentiate way as the IIR case rather than a closed-form shortcut, since that also handles a non-symmetric FIR correctly.

From the note above this builtin in the interpreter, where the reasoning was written down as it was built.