Frequency

DFT of signal with frequency-dependent time shift

DFT of signal with frequency-dependent time shift
  1. How does a time shift affect frequency domain?
  2. What happens to the spectrum of signal in frequency domain if there is a time delay in time domain?
  3. How do you calculate DFT frequency?
  4. Which property of DFT provides energy of signal in time and frequency domain?

How does a time shift affect frequency domain?

Apparently, a shift in the time domain corresponds to a phase rotation in the frequency domain. In particular, when the time-shift equal 1s (or in general: t0), the period of the phase rotation in frequency domain amounts 1Hz (or in general 1/t0Hz).

What happens to the spectrum of signal in frequency domain if there is a time delay in time domain?

the signal will be same so same frequency content but our time t=0 has already started 1 sec before so waveform will only shift by 1 sec right i.e phase not frequency component.

How do you calculate DFT frequency?

calculate the magnitude of each DFT output bin: magnitude = sqrt(re*re+im*im) find the bin with the largest magnitude, call its index i_max . calculate the equivalent frequency of this bin: freq = i_max * Fs / N , here Fs = sample rate (Hz) and N = no of points in FFT.

Which property of DFT provides energy of signal in time and frequency domain?

Periodicity property of DFT in time and frequency domain.

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