Frequency Response Flashcards
Sampling theorem and Nyquist frequency
perfect reconstruction is possible for bandlimited signals if the signal is sampled at a frequency greater or equal to twice the maximum signal frequency. The Nyquist frequency is defined to be half the sampling frequency.
State what is meant by aliasing and describe why it occurs. Explain how to reduce aliasing if the continuous-time signal is not band-limited.
Aliasing occurs due to the periodicity of the sampled spectrum in the frequency domain –
this periodicity occurs due to the uniform time sampling of a continuous-time signal. The
sampled spectrum is periodic with a period equal to the sampling frequency with the baseband
of the continuous-time signal repeating at the sampling frequency. If the bandwidth of the
continuous-time signal is greater than the Nyquist frequency (half the sampling rate) then
adjacent basebands overlap and sum resulting in distortion; in this case the signal can no longer
be perfectly reconstructed from the samples. Most signals are not strictly band limited and hence
analogue anti-aliasing filters are used to restrict the bandwidth of the signal and the Nyquist
frequency is set greater than the cut off frequency of the filter
effect of window
when you window a function, convolution of window is sinc, amplitude infinite decreasing humps, therefore output frequency spectrum contains small high frequencies that get aliased.
