This document provides an introduction and overview of digital signal processing. It discusses the differences between analog and digital signal processing, different types of signals, and comparisons between continuous-time and discrete-time signals. It also covers characteristics of discrete-time sinusoids, limitations of digital signal processing, and analog to digital and digital to analog conversion.

2. Contents
Introduction to Digital Signal Processing
Analog Signal Processing Versus Digital Signal
Processing
Classification Of Signals
Comparison Between Continuous-Time & Discrete-Time
Sinusoids
Characteristics Of Discrete-time Sinusoids
A/D and D/A Conversion

3. Signal
A signal is any physical quantity that varies with time, space or any
other independent variable or variables.
Real-valued, Complex valued, multichannel, multi-diemnsional
Processing
Performing certain operations on a signal to extract some useful
information
Digital
The word digital in digital signal processing means that the
processing is done either by a digital hardware or by a digital
computer.

4. Digital Signal Processing is performing signal processing using digital
techniques with the aid of digital hardware and/or some kind of
computing device.
Digital Signal Processor is a digital computer or processor that is
designed especially for signal processing applications.

5. Accuracy limitations due to
 Component tolerances
 Undesired nonlinearities
Limited repeatability due to
 Tolerances
 Changes in environmental conditions
 Temperature
 Vibration
Sensitivity to electrical noise
Limited dynamic range for voltage and currents
Inflexibility to changes
Difficulty of storing information

6. Accuracy can be controlled by choosing word length
Repeatable
Sensitivity to electrical noise is minimal
Dynamic range can be controlled using floating point numbers
Flexibility can be achieved with software implementations
Digital storage is cheap
Digital information can be encrypted for security

7. Limitations of Digital Signal Processing
 Sampling causes loss of information
 A/D and D/A requires mixed-signal hardware
 Limited speed of processors
 Quantization and round-off errors

8. Signal
Continuous
Time
Signal
Discrete
Time Signal
Continuous
Valued
Signal
Discrete
Valued
Signal

9. Continuous-Time Signal
Function of time
Finite or Infinite values
Discrete-Time Signal
Function of n (number of samples)
Finite or Infinite values
Continuous-Valued Signal
Infinite values
Function of time or n
Discrete-Valued Signal
Finite values
Function of time or n

10. Continuous-Time Signals (Analog signal) are defined for every value
of time. It is represented as a function of time.
Where as
Discrete-Time Signals are defined only at certain specific values of
time. It is represented as a function of n (number of samples).

11. Comparison Between Continuous
Time and Discrete Time Signal
Continuous Time
x(t) = A cos(Ωt +θ ) , - ∞ < t < ∞
Ω = 2π F -∞ < F < ∞
Where
A= Amplitude
Ω = Frequency (radian/ second)
θ=Phase
F=cycles/second
Discrete Time
x (n) = A cos(ω n+ θ) - ∞ < n< ∞
ω =2π f -π ≤ ω ≤ π
Where
A = Amplitude
ω = Frequency (radian/sample)
θ = Phase
f = cycles/sample

12. 1. A Discrete-time sinusoid is periodic if its frequency f is a rational
number.
2. Discrete-time sinusoids whose frequencies are separated by an integer
multiple of 2π are identical.
3. The highest rate of oscillation in a discrete-time sinusoid is attained
when ω = π ( or ω = -π) or, equivalently f=1/2 (or f= -1/2).

13. A Discrete-time sinusoid is periodic if its frequency f is a
rational number.

14. Discrete-time sinusoids whose frequencies are separated by
an integer multiple of 2π are identical.
Consider the sinusoid
It follows
Where
are indistinguishable(i.e. identical).
The sinusoids having the frequency | 𝝎|> 𝝅 are the alias of the
corresponding sinusoid with frequency | 𝝎|< 𝝅.

15. The highest rate of oscillation in a discrete-time sinusoid is
attained when ω = π ( or ω = -π) or, equivalently f=1/2 (or f= -1/2).

17. Example # 1:
x (n) = A cos(ω n+ θ)
Where
ω = π/6 and θ=π/3
f = 1/12 cycles per sample