How to generate a lower frequency version of a signal in Matlab?

Question

With a sine input, I tried to modify it's frequency cutting some lower frequencies in the spectrum, shifting the main frequency towards zero. As the signal is not fftshifted I tried to do that by eliminating some samples at the begin and at the end of the fft vector:

interval = 1;
samplingFrequency = 44100;
signalFrequency = 440;
sampleDuration = 1 / samplingFrequency;
timespan = 1 : sampleDuration : (1 + interval);
original = sin(2 * pi * signalFrequency * timespan);
fourierTransform = fft(original);
frequencyCut = 10; %% Hertz
frequencyCut = floor(frequencyCut * (length(pattern) / samplingFrequency) / 4); %% Samples
maxFrequency = length(fourierTransform) - (2 * frequencyCut);
signal = ifft(fourierTransform(frequencyCut + 1:maxFrequency), 'symmetric');

But it didn't work as expected. I also tried to remove the center part of the spectrum, but it wielded a higher frequency sine wave too.

How to make it right?

Answer 1

@las3rjock:

its more like downsampling the signal itself, not the FFT.. Take a look at downsample.

Or you could create a timeseries object, and resample it using the resample method.

EDIT:

a similar example :)

% generate a signal
Fs = 200;
f = 5;
t = 0:1/Fs:1-1/Fs;
y = sin(2*pi * f * t) + sin(2*pi * 2*f * t) + 0.3*randn(size(t));

% downsample
n = 2;
yy = downsample([t' y'], n);

% plot
subplot(211), plot(t,y), axis([0 1 -2 2])
subplot(212), plot(yy(:,1), yy(:,2)), axis([0 1 -2 2])

Answer 2

A crude way to downsample your spectrum by a factor of n would be

% downsample by a factor of 2
n = 2; % downsampling factor
newSpectrum = fourierTransform(1:n:end);

For this to be a lower-frequency signal on your original time axis, you will need to zero-pad this vector up to the original length on both the positive and negative ends. This will be made much simpler using fftshift:

pad = length(fourierTransform);
fourierTransform = [zeros(1,pad/4) fftshift(newSpectrum) zeros(1,pad/4)];

To recover the downshifted signal, you fftshift back before applying the inverse transform:

signal = ifft(fftshift(fourierTransform));

EDIT: Here is a complete script which generates a plot comparing the original and downshifted signal:

% generate original signal
interval = 1;
samplingFrequency = 44100;
signalFrequency = 440;
sampleDuration = 1 / samplingFrequency;
timespan = 1 : sampleDuration : (1 + interval);
original = sin(2 * pi * signalFrequency * timespan);

% plot original signal
subplot(211)
plot(timespan(1:1000),original(1:1000))
title('Original signal')

fourierTransform = fft(original)/length(original);

% downsample spectrum by a factor of 2
n = 2; % downsampling factor
newSpectrum = fourierTransform(1:n:end);

% zero-pad the positive and negative ends of the spectrum
pad = floor(length(fourierTransform)/4);
fourierTransform = [zeros(1,pad) fftshift(newSpectrum) zeros(1,pad)];

% inverse transform
signal = ifft(length(original)*fftshift(fourierTransform),'symmetric');

% plot the downshifted signal
subplot(212)
plot(timespan(1:1000),signal(1:1000))
title('Shifted signal')

Plot of original and downshifted signals http://img5.imageshack.us/img5/5426/downshift.png