Linearity and time-shifting of $\mathcal{F}\{0.8^n\cos(0.1πn)u[n]\}$

1. What is time shifting in Fourier series?
2. What is linearity in Fourier transform?
3. How do you shift in frequency domain?
4. What is time scaling property?

What is time shifting in Fourier series?

The time-shifting property identifies the fact that a linear displacement in time corresponds to a linear phase factor in the frequency domain. This becomes useful and important when we discuss filtering and the effects of the phase characteristics of a filter in the time domain.

What is linearity in Fourier transform?

Linearity: Addition of two functions corresponding to the addition of the two frequency spectrum is called the linearity. If we multiply a function by a constant, the Fourier transform of the resultant function is multiplied by the same constant.

How do you shift in frequency domain?

Multiplying a function with a complex exponential with period t0=1/f0, corresponds to shifting the frequency domain by 1/t0=f0.

What is time scaling property?

Statement – The time-scaling property of Fourier transform states that if a signal is expended in time by a quantity (a), then its Fourier transform is compressed in frequency by the same amount. Therefore, if. x(t)FT↔X(ω)