Frequency shift using FFT in Matlab

Question

I am working on implementing BFSK modulation and demodulation with frequency hopping and I need to test my results using Matlab. The output the I am getting from my BFSK program is an array of sine values corresponding to the carrier signal for different bits. These signals are passband signals centered at 2.51KHz with a band width of 4KHz around it. But to test the demodulation step, I need to convert the signal to baseband. So I need to center my output signal at 0Hz.

I know that creating a complex signal of 2.51KHz and multiplying it in time-domain would do this job. But is there any method that I can use with fft() function in matlab to shift the center frequency of the signal and then take an ifft() of the signal to generate the baseband signal.

Thanks, Anshu

Answer 1

This should be perfectly possible. Just rotate the complex vector that emerges from the fft process before computing the ifft.

Pseudocode would be:

shiftIndex  = 20; %// This value would depend on the frequency shift requited

Y = fft(x); %// Where x is the input vector
z = ifft (  [Y((shiftIndex+1):end);      Y(1:shiftIndex)]  );

For help on the number of bins that you'd need to shift the index by, you might find the following question useful . . .

https://dsp.stackexchange.com/questions/2970/how-to-make-frequency-axis-for-even-and-odd-fft-length/2971#2971

This reminds me, you'd probably get quicker answers posting questions like this on DSP.stackexchange.com in the future.