- DSP - Miscellaneous Signals
- DSP - Classification of DT Signals
- DSP - Classification of CT Signals
- DSP - Basic DT Signals
- DSP - Basic CT Signals
- DSP - Signals-Definition
- DSP - Home
Operations on Signals
- Operations Signals - Convolution
- Operations Signals - Integration
- Operations Signals - Differentiation
- Operations Signals - Reversal
- Operations Signals - Scaling
- Operations Signals - Shifting
Basic System Properties
- DSP - Solved Examples
- DSP - Unstable Systems
- DSP - Stable Systems
- DSP - Time-Variant Systems
- DSP - Time-Invariant Systems
- DSP - Non-Linear Systems
- DSP - Linear Systems
- DSP - Anti-Causal Systems
- DSP - Non-Causal Systems
- DSP - Causal Systems
- DSP - Dynamic Systems
- DSP - Static Systems
Z-Transform
- Z-Transform - Solved Examples
- Z-Transform - Inverse
- Z-Transform - Existence
- Z-Transform - Properties
- Z-Transform - Introduction
Discrete Fourier Transform
- DFT - Solved Examples
- DFT - Discrete Cosine Transform
- DFT - Sectional Convolution
- DFT - Linear Filtering
- DTF - Circular Convolution
- DFT - Time Frequency Transform
- DFT - Introduction
Fast Fourier Transform
Digital Signal Processing Resources
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DSP - Operations on Signals Shifting
Shifting means movement of the signal, either in time domain (around Y-axis) or in ampptude domain (around X-axis). Accordingly, we can classify the shifting into two categories named as Time shifting and Ampptude shifting, these are subsequently discussed below.
Time Shifting
Time shifting means, shifting of signals in the time domain. Mathematically, it can be written as
$$x(t) ightarrow y(t+k)$$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
![Time Shifting Case1 Example](/digital_signal_processing/images/time_shifting_case1_example.jpg)
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.
![Time Shifting Case2 Example](/digital_signal_processing/images/time_shifting_case2_example.jpg)
Ampptude Shifting
Ampptude shifting means shifting of signal in the ampptude domain (around X-axis). Mathematically, it can be represented as −
$$x(t) ightarrow x(t)+K$$This K value may be positive or negative. Accordingly, we have two types of ampptude 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;
$$x = egin{cases}0, & t < 0\1, & 0leq tleq 2\ 0, & t>0end{cases}$$Let we have taken K=+1 so new signal can be written as −
$y(t) ightarrow x(t)+1$ So, y(t) can finally be written as;
$$x(t) = egin{cases}1, & t < 0\2, & 0leq tleq 2\ 1, & t>0end{cases}$$![Ampptude Shifting Case1 Example](/digital_signal_processing/images/ampptude_shifting_case1_example.jpg)
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;
$$x(t) = egin{cases}0, & t < 0\1, & 0leq tleq 2\ 0, & t>0end{cases}$$Let we have taken K = -1 so new signal can be written as;
$y(t) ightarrow x(t)-1$ So, y(t) can finally be written as;
$$y(t) = egin{cases}-1, & t < 0\0, & 0leq tleq 2\ -1, & t>0end{cases}$$![Ampptude Shifting Case2 Example](/digital_signal_processing/images/ampptude_shifting_case2_example.jpg)