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# goertzel() - Signal Processing

```dft_data = goertzel(data) returns the discrete
Fourier transform (DFT) of the input data, data,
using a second-order Goertzel algorithm. If data is
a matrix, goertzel computes the DFT of each column
separately.dft_data = goertzel(data,freq_indices) returns
the DFT for the frequency indices freq_indices. dft_data = goertzel(data,freq_indices,dim) computes
the DFT of the matrix data along the dimension dim.```

### Syntax

`dft_data = goertzel(data)dft_data = goertzel(data,freq_indices)dft_data = goertzel(data,freq_indices,dim)`

### Example

```Estimate Telephone Keypad FrequenciesOpen This Example
Estimate the frequencies of the tone generated by pressing the 1 button on a telephone keypad.
The number 1 produces a tone with frequencies 697 and 1209 Hz. Generate 205 samples of the tone with a sample rate of 8 kHz.Fs = 8000;
N = 205;
lo = sin(2*pi*697*(0:N-1)/Fs);
hi = sin(2*pi*1209*(0:N-1)/Fs);
data = lo + hi;
Use the Goertzel algorithm to compute the DFT of the tone. Choose the indices corresponding to the frequencies used to generate the numbers 0 through 9.f = [697 770 852 941 1209 1336 1477];
freq_indices = round(f/Fs*N) + 1;
dft_data = goertzel(data,freq_indices);
Plot the DFT magnitude.stem(f,abs(dft_data))

ax = gca;
ax.XTick = f;
xlabel('Frequency (Hz)')
title('DFT Magnitude')

Resolve Frequency Components of a Noisy ToneOpen This ExampleGenerate a noisy cosine with frequency components at 1.24 kHz, 1.26 kHz, and 10 kHz. Specify a sample rate of 32 kHz. Reset the random number generator for reproducible results.rng default

Fs = 32e3;
t = 0:1/Fs:2.96;
x = cos(2*pi*t*10e3) + cos(2*pi*t*1.24e3) + cos(2*pi*t*1.26e3) ...
+ randn(size(t));
Generate the frequency vector. Use the Goertzel algorithm to compute the DFT. Restrict the range of frequencies to between 1.2 and 1.3 kHz.N = (length(x)+1)/2;
f = (Fs/2)/N*(0:N-1);
indxs = find(f>1.2e3 & f<1.3e3);
X = goertzel(x,indxs);
Plot the mean squared spectrum expressed in decibels.plot(f(indxs)/1e3,mag2db(abs(X)/length(X)))

title('Mean Squared Spectrum')
xlabel('Frequency (kHz)')
ylabel('Power (dB)')
grid```