What happens to the Fourier transform of a signal when it is compressed in time?

What happens to the Fourier transform of a signal when it is compressed in time?

Chapter 10: Fourier Transform Properties. As shown in Fig. 10-12, a compression of the signal in one domain results in an expansion in the other, and vice versa. If an event happens faster (it is compressed in time), it must be composed of higher frequencies.

What is the need of fast Fourier transform in DSP?

The DFT converts a time-domain sequence into an equivalent frequency-domain sequence. The FFT is a very efficient algorithm technique based on the DFT but with fewer computations required. The FFT is one of the most commonly used operations in digital signal processing to provide a frequency spectrum analysis [1–6].

How does shifting a signal in the time domain affect its frequency domain?

How does shifting a signal in the time domain affect its frequency domain? Suppose the signal is shifted by dt (signal ‘starts’ later, say after 1s instead of 0s), does that correspond to a positive or a negative phase shift df in the frequency domain?

How does padding by zeroes work in frequency domain?

Your padding by zeroes operation is essentially the same as taking an extended set of points of the original time series and multiplying it by a rectangular function (whose non zero region is limited to the points x 0, … x N − 1 ). Therefore, in the frequency domain your original DFT is convolved by a sinc function.

How is padding by zeroes used in Fourier transform?

Your padding by zeroes operation is essentially the same as taking an extended set of points of the original time series and multiplying it by a rectangular function (whose non zero region is limited to the points $x_0,ldots x_{N-1}$).

How is frequency domain analysis used in Electrical Engineering?

Frequency domain analysis and Fourier transforms are a cornerstone of signal and system analysis. These ideas are also one of the conceptual pillars within electrical engineering. Among all of the mathematical tools utilized in electrical engineering, frequency domain analysis is arguably the most far-reaching.