- #1
bonildo
- 14
- 1
Whais is the effect of a multiplication by (-1)^n in the DTFT ??
In other words, what's is this transform : x(n)* (-1)^n ??
In other words, what's is this transform : x(n)* (-1)^n ??
The DTFT (Discrete-Time Fourier Transform) of x(n)*(-1)^n is a mathematical operation that transforms a discrete-time signal x(n) that is multiplied by the alternating sequence (-1)^n into the frequency domain. This means that the resulting DTFT will show the frequency components present in the signal x(n) after it has been multiplied by (-1)^n.
The effect of multiplying a signal by (-1)^n is a phase inversion. This means that every other sample of the signal will be inverted or flipped in the opposite direction. For example, if the original signal had a positive amplitude, the sample after multiplication will have a negative amplitude.
The DTFT of x(n)*(-1)^n and the DTFT of x(n) will have the same frequency components, but the phase of each component will be inverted in the DTFT of x(n)*(-1)^n. This is due to the phase inversion caused by multiplying the signal by (-1)^n.
Yes, the DTFT of x(n)*(-1)^n can be used to analyze signals in the frequency domain. It can be used to identify the frequency components present in the signal after it has been multiplied by (-1)^n. This can be useful in applications such as signal processing and filtering.
Yes, the DTFT of x(n)*(-1)^n is reversible. This means that the original signal x(n) can be recovered by performing an inverse DTFT on the DTFT of x(n)*(-1)^n. However, the recovered signal will have a phase inversion compared to the original signal due to the multiplication by (-1)^n.