how to use the fft and fftshift commands ?

generate a 10 kHz sinusoid sampled at 100 kHz. Plot four cycles of the signal. Also plot the spectrum of this signal in the interval (-π, π). Use the fft and fftshift commands for this purpose. The horizontal axis must be scaled appropriately to represent the interval (-π, π).

Answer 1

[Image Analyst]

Use the formula y = amplitude * sin(2*pi*frequency*t). You might also like to use t = linspace(-pi, pi, n). Figure out what n needs to be to get 4 cycles of the 10 kHz sine wave.

Of course if the t axis goes from -pi to +pi seconds, then 4 cycles of a 10 kHz sine wave will take up a very very small portion of your signal, just 4 ten thousandths of a second - barely visible in the much wider 2*pi plot. So your signal is essentially masked by a rect function. Perhaps it does this so you'll notice a sinc function modulation on the Fourier spectrum rather than just two narrow delta function spikes.