Shifting - Operations on Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE) PDF Download

Shifting means movement of the signal, either in time domain (around Y-axis) or in amplitude domain (around X-axis). Accordingly, we can classify the shifting into two categories named as Time shifting and Amplitude shifting, these are subsequently discussed below.

Time Shifting

Time shifting means, shifting of signals in the time domain. Mathematically, it can be written as

Shifting - Operations on Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

This K value may be positive or it may be negative. According to the sign of k value, we have two types of shifting named as Right shifting and Left shifting.

Case 1 (K > 0)

When K is greater than zero, the shifting of the signal takes place towards "left" in the time domain. Therefore, this type of shifting is known as Left Shifting of the signal.

Example

Shifting - Operations on Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

Case 2 (K < 0)

When K is less than zero the shifting of signal takes place towards right in the time domain. Therefore, this type of shifting is known as Right shifting.

Example

The figure given below shows right shifting of a signal by 2.

Shifting - Operations on Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

Amplitude Shifting

Amplitude shifting means shifting of signal in the amplitude domain (around X-axis). Mathematically, it can be represented as −

Shifting - Operations on Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

This K value may be positive or negative. Accordingly, we have two types of amplitude shifting which are subsequently discussed below.

Case 1 (K > 0)

When K is greater than zero, the shifting of signal takes place towards up in the x-axis. Therefore, this type of shifting is known as upward shifting.

Example

Let us consider a signal x(t) which is given as;

Shifting - Operations on Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

Let we have taken K=+1 so new signal can be written as −

Shifting - Operations on Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE) So, y(t) can finally be written as;

Shifting - Operations on Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

Shifting - Operations on Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

Case 2 (K < 0)

When K is less than zero shifting of signal takes place towards downward in the X- axis. Therefore, it is called downward shifting of the signal.

Example

Let us consider a signal x(t) which is given as;

Shifting - Operations on Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

Let we have taken K = -1 so new signal can be written as;

Shifting - Operations on Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE) So, y(t) can finally be written as;

Shifting - Operations on Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)
Shifting - Operations on Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

The document Shifting - Operations on Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE) is a part of the Electronics and Communication Engineering (ECE) Course Digital Signal Processing.
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FAQs on Shifting - Operations on Signals - Digital Signal Processing - Electronics and Communication Engineering (ECE)

1. What is shifting in the context of operations on signals?
Ans. Shifting, in the context of operations on signals, refers to the process of moving or displacing a signal horizontally along the time axis. It involves delaying or advancing the signal in time by a certain amount.
2. How is shifting performed on signals?
Ans. Shifting is performed on signals by introducing a time delay or advance. The signal is shifted to the right by delaying it, or to the left by advancing it, along the time axis. This can be achieved by multiplying the signal with a complex exponential function, which introduces the desired time shift.
3. What are the applications of shifting in signal processing?
Ans. Shifting has various applications in signal processing. It is commonly used in audio processing to create effects like echo or reverb. In image processing, shifting can be used for image alignment or registration. Shifting is also utilized in communication systems to compensate for propagation delays or synchronize signals.
4. How does shifting affect the frequency content of a signal?
Ans. Shifting a signal in time does not directly affect its frequency content. The frequency spectrum of the signal remains unchanged. However, shifting can lead to phase shifts in the frequency domain, altering the relative phase relationship between different frequency components.
5. Are there any limitations or considerations when performing shifting operations on signals?
Ans. Yes, there are certain limitations and considerations when performing shifting operations on signals. Shifting can introduce artifacts or distortion if not properly applied. It is important to ensure that the shifted signal does not overlap with itself or other parts of the signal, as this can lead to interference or aliasing. Additionally, the amount of shift should be within the range of the signal's duration to avoid truncation or loss of information.
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