The document presents an overview of basic digital signal processing (DSP) operations, including time shifting, time reversal, time scaling, and amplitude scaling. It details how these operations manipulate digital signals and provides examples and mathematical representations for each operation. Various applications of these operations, such as filtering and signal reconstruction, are also discussed.

2. DIGITAL SIGNAL PROCESSING
Presented by Group-9

3. Our Team
Rabiul
Limon
Mehedi
Sofikul
Pithu

4. Topics
Basic DSP Operation
Time Shifting
Time Reversal
Time Scaling

5. Basic Digital Signal Processing (DSP) operations are fundamental mathematical
and computational processes used to manipulate digital signals.
It can be applied to both discrete-time signals and continuous-time signals,
although it is more commonly associated with discrete signals due to the nature
of digital systems and computation.
As the D-T signals based on the two variables (amplitude and time ), the basic
operations are :
● Time shifting operation .
● Time reversal or folding operation.
● TIme scaling operation .
● Amplitude scaling operation
Basic Digital Signal Processing
Operation

6. Here are some examples of how the basic DSP operations
mentioned earlier are used in various applications:
1. Filtering
2. Convolution
3. Discrete Fourier Transform (DFT) and Fast Fourier
Transform (FFT)
4. Sampling and Quantization
5. Modulation and Demodulation
6. Signal Reconstruction

7. TIME SHIFTING
Time shifting refers to the operation of shifting a signal along the time axis by a certain
amount. Time shifting modifies the temporal alignment of a signal without altering its
amplitude or shape.
Mathematically, time shifting can be represented as :
Input Output
x[n] y[n]= x[n-k]
Where k=Integer = +ve or -ve
Types of Time Shifting :
1. Delay (when k= +ve)
2. Advance (when k= -ve)
Time Shifting Operation

8. Delay
Example:
x(n)={....0,0,-2, 0, 1, -3 , +2, -1, +3….}
y(n) = x(n-3) = {...0, 0, -2, 0, +1, -3, +2, -1, +3,0, 0….}
Here , k=+3,
So , Time delaying

9. Advance
Example:
x(n)={....0,0,-2, 0, 1, -3 , +2, -1, +3….}
y(n) = x(n+2)={....0, -2, 0, 1, -3, +2, -1, +3,0…..}
Here , k=-2,
So , Time advancing

10. TIME REVERSING
Time-reversing is a fundamental operation that involves reversing the order of samples in a
signal with respect to time. This operation can be applied to both discrete-time signals and
continuous-time signals, although in DSP, it's primarily discussed in the context of discrete-time
signals.
Mathematically, time reversing can be represented as :
Input Output
x[n] y[n]= x[-n]
The output function resulting from time-reversal as being a mirrored version of the input
function with respect to time.It effectively flips the signal around a vertical axis located at
the midpoint of the signal's duration.
Time Reversing Operation

11. Time Reversing
Example:
x(n)={....0, 0, 0, 1, 2, 3, 2, 1, 0, 0 ….}
y(n) = x(-n)
So, y(n)= {...0, 0, 1, 2 ,3 , 2, 1, 0 , 0…..}
Time reversing graph

12. Time Scaling
Time scaling refers to the process of altering the rate at which a signal progresses
through time without changing its fundamental characteristics. It involves
compressing or expanding the time axis of a signal.
Mathematically, For a discrete-time signal x[n], time scaling by a factor α results in
a new signal y[n] given by:-
y[n] = x[αn]
Types of Time Scaling:
1. Compression (when α>1 )
2. Expansion (when α<1)

13. Compression
Example:
x(n)={...0,1,2,3,4,3,2,1,0…….}
y(n) = x(2n)
Here, α =2
So, y(n)={..0, 2 , 4, 2, 0…}
Time compression

14. Expansion
Example:
x(n)={...0,0,1,2,3,4,3,2,1,0…….}
y(n) = x(n/2)
Here, α =½
y(n)= {...0,2,0,3,0,4,0,3,0,2,0….}
Time Expansion

15. Question
Time