DIGITAL SIGNAL PROCESSING
Presented by Group-9
Our Team
Pithu
Sofikul
Rabiul Mehedi
Limon
Topics
Basic DSP Operation
Time Shifting
Time Reversal
Time Scaling
Basic Digital Signal Processing
Operation
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
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
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] Time Shifting Operation 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)
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
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
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] Time Reversing Operation
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
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
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)
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
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
Question
Time
