goertzel_freq

Builtin index · Signal processing

result = goertzel_freq(x, fs, freq)

Input: x, fs, freq · Output: result

What it is

x is a length-N real vector; fs (number, Hz) is the sample rate; freq is the frequency to evaluate (a number, Hz) or a length-K vector of frequencies.

Overloads

One call shape — this function is not overloaded.

Code	Input	Output	Description
`result = goertzel_freq(x, fs, freq)`	`x` vector`x` is a length-N real vector. `fs` number`fs` (number, Hz) is the sample rate. `freq` number or vector`freq` is the frequency to evaluate (a number, Hz) or a length-K vector of frequencies.	`result` scalar or CVec	Returns a single complex scalar or a length-K `CVec`, same batching as `goertzel` above. `goertzel` parameterized by real frequencies rather than raw bin indices — the common case of checking one or several known tone frequencies at a fixed sample rate.

Examples

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

  fs = 8000
  tone_hz = 941                  # one DTMF tone

  strength = abs(goertzel_freq(samples, fs, tone_hz))

from numerics-dsp

fs = 1000
n = 0:1:63
t = n / fs
x = sin(2*pi*100*t)

X = fft(x)
xr = idft(X)
print("idft roundtrip max err: {max(abs(xr - x))}")

k100 = 100 * length(x) / fs        # bin index equivalent to 100 Hz

bin100 = goertzel(x, k100)
print("goertzel magnitude at bin {k100}: {abs(bin100)}")
same = goertzel_freq(x, fs, 100)   # the Hz-parameterized convenience form

print("goertzel_freq agrees: {abs(same - bin100) < 1e-9}")

half = rfft(x)
back = irfft(half, 64)
print("rfft/irfft roundtrip max err: {max(abs(back - x))}")

output

idft roundtrip max err: 1.604386e-14
goertzel magnitude at bin 6.4: 32.158025
goertzel_freq agrees: true
rfft/irfft roundtrip max err: 3.330669e-16

from signal-processing

How it works

goertzel_freq(x, fs, freq) -- goertzel parameterized by a real frequency in Hz rather than a raw bin index, the common case (a known tone frequency at a fixed sample rate). freq may also be a vector of frequencies, same K-point-DFT batching as goertzel above, returning a CVec.

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