- Digital Signal Processing Tutorial
- DSP - Home
- DSP - Signals-Definition
- DSP - Basic CT Signals
- DSP - Basic DT Signals
- DSP - Classification of CT Signals
- DSP - Classification of DT Signals
- DSP - Miscellaneous Signals

- Operations on Signals
- Operations Signals - Shifting
- Operations Signals - Scaling
- Operations Signals - Reversal
- Operations Signals - Differentiation
- Operations Signals - Integration
- Operations Signals - Convolution

- Basic System Properties
- DSP - Static Systems
- DSP - Dynamic Systems
- DSP - Causal Systems
- DSP - Non-Causal Systems
- DSP - Anti-Causal Systems
- DSP - Linear Systems
- DSP - Non-Linear Systems
- DSP - Time-Invariant Systems
- DSP - Time-Variant Systems
- DSP - Stable Systems
- DSP - Unstable Systems
- DSP - Solved Examples

- Z-Transform
- Z-Transform - Introduction
- Z-Transform - Properties
- Z-Transform - Existence
- Z-Transform - Inverse
- Z-Transform - Solved Examples

- Discrete Fourier Transform
- DFT - Introduction
- DFT - Time Frequency Transform
- DTF - Circular Convolution
- DFT - Linear Filtering
- DFT - Sectional Convolution
- DFT - Discrete Cosine Transform
- DFT - Solved Examples

- Fast Fourier Transform
- DSP - Fast Fourier Transform
- DSP - In-Place Computation
- DSP - Computer Aided Design

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# DSP - Operations on Signals Shifting

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

$$x(t) \rightarrow y(t+k)$$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**

### 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.

## Amplitude Shifting

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

$$x(t) \rightarrow x(t)+K$$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;

$$x = \begin{cases}0, & t < 0\\1, & 0\leq t\leq 2\\ 0, & t>0\end{cases}$$Let we have taken K=+1 so new signal can be written as −

$y(t) \rightarrow x(t)+1$ So, y(t) can finally be written as;

$$x(t) = \begin{cases}1, & t < 0\\2, & 0\leq t\leq 2\\ 1, & t>0\end{cases}$$### 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;

$$x(t) = \begin{cases}0, & t < 0\\1, & 0\leq t\leq 2\\ 0, & t>0\end{cases}$$Let we have taken K = -1 so new signal can be written as;

$y(t)\rightarrow x(t)-1$ So, y(t) can finally be written as;

$$y(t) = \begin{cases}-1, & t < 0\\0, & 0\leq t\leq 2\\ -1, & t>0\end{cases}$$