matlab,signal-processing,wavelet,wavelet-transform,continuous-fourier

Because we are dealing with digitized signals. You can not plot an infinite amount of samples of your signal. That is why you need to specify some parameters prior to working with digitized signals, such as the sampling frequency. The sampling frequency gives you a relationship between your samples indices...

matlab,signal-processing,fft,frequency,continuous-fourier

I can't get your pictures to load over my proxy, but the spectrum of a FFT will be have a bigger "gap" in the middle at a higher sampling rate. A fundamental property of sampling is that it introduces copies of your original spectrum; you may have learned this if...