Nyquist Filters
Under certain conditions, a lowpass filter
can be designed to have a number of zerovalued coefficients
When used as interpolation filters these
filters preserve the nonzero samples of the
up-sampler output at the interpolator output
Mor

Mid Semester Examination, September 2010
B. Tech. Semester VII (EC)
2EC402: Digital Signal Processing
Instruction: Please be specific and concise in your answer i.e. write only what is
asked.
1 A
Give reasoning of any six of the following:
(i) The digital

Mid Semester Examination, September 2011
B. Tech. Semester V (EC)
2EC402: Digital Signal Processing
Date and Time: 2/9/2011
9.30 AM to 11 AM
Max. Marks: 50
Q.1 A State any five properties of DFT or z-Transform and prove any one of those.
B Find the invers

Institute of Technology, Nirma University
Adaptive Signal Processing
Handout #
Finite impulse response
A finite impulse response (FIR) filter is a type of a digital filter. The impulse response,
the filter's response to a Kronecker delta input, is finite

Contents
Preface
1
vii
Discrete-Time Signals in the Time Domain
1.1 Introduction
1
1.2 Getting Started
1
1.3 Background Review
2
1.4 MATLAB Commands Used
5
1.5 Generation of Sequences
5
1.6 Simple Operations on Sequences
1.7 Workspace Information
1.9 Back

Institute of Technology, Nirma University
Adaptive Signal Processing
Handout #
Infinite impulse response
Infinite impulse response (IIR) is a property of signal processing systems. Systems with
this property are known as IIR systems or, when dealing with

Signals and Systems
Chapter SS-5
The Discrete-Time Fourier Transform
N P Gajjar
NU-EC
Figures and images used in these lecture notes are adopted from
Signals & Systems by Alan V. Oppenheim and Alan S. Willsky, 1997
Outline
DTFT - 2
Representation of Aperi

Signals and Systems
The Continuous-Time Fourier Transform
Nagendra Gajjar
NU-EE
July 2009
Figures and images used in these lecture notes are adopted from
Signals & Systems by Alan V. Oppenheim and Alan S. Willsky, 1997
Outline
CTFT - 2
Representation of A

Signals and Systems
Fourier Series Representation
of Periodic Signals
Nagendra Gajjar
NU-EE
July 2009
Figures and images used in these lecture notes are adopted from
Signals & Systems by Alan V. Oppenheim and Alan S. Willsky, 1997
Outline
FS - 2
A Histori

6x9 Handbook / Radar Handbook / Skolnik / 148547-3 / Chapter 25
Chapter 25
Radar Digital
Signal Processing
James J. Alter
Jeffrey O. Coleman
Naval Research Laboratory
25.1 INTRODUCTION
The exponential growth in digital technology since the 1980s, along wi

Signals and Systems
Linear Time-Invariant Systems
Nagendra Gajjar
NU-ECE
July 2009
Figures and images used in these lecture notes are adopted from
Signals & Systems by Alan V. Oppenheim and Alan S. Willsky, 1997
Outline
LTI - 2
Discrete-Time Linear Time-I

DigitalSignalProcessingImportantConcepts
(1)Sampling:
ForlowpasssignalbandlimitedtoBHzbypassingoriginalsignalthroughantialiazingfilteroflowpassbandwidthBHz
andalsoforbandpasssignalwithbandwidthBHz,samplingshouldbeperformedatfrequencyatleast2Bsamples/s.
Or

Institute of Technology, Nirma University
Adaptive Signal Processing
Handout #
Digital filter
A general finite impulse response filter with n stages, each with an independent delay, di,
and amplification gain, ai.
In electronics, computer science and math

Institute of Technology, Nirma University
Adaptive Signal Processing
Handout #
Autocorrelation
Autocorrelation is the cross-correlation of a signal with itself. It is a mathematical tool
for finding repeating patterns, such as the presence of a periodic s

Discrete Multitone Transmission
Binary data are normally transmitted serially
as a pulse train as indicated below
+1
a0
a1
a2
a3
a4
a5
Discrete Multitone Transmission
For example, the pulse train shown in the
previous slide arriving at the receiver may

Musical Sound Processing
Almost all musical programs are produced
basically in two stages:
(1) Sound from each individual intrument is
recorded in an acoustically inert studio on a
single track of a multitrack tape recorder
(2) Signals from each track

Oversampling A/D Converter
Oversampling A/D Converter
For digital processing of an analog continuoustime signal, the signal is first passed through a
S/H circuit whose output is then converted into
a digital form by means of an A/D converter
According t

Polyphase Decomposition
Polyphase Decomposition
The Decomposition
Consider an arbitrary sequence cfw_x[n] with
a z-transform X(z) given by
X ( z ) = = x[n]z n
n
We can rewrite X(z) as
M
X ( z ) = k =1 z k X k ( z M )
0
where
X k ( z ) = = xk [n] z n = =

Up-Sampler
Multirate Digital Signal
Processing
Time-Domain Characterization
An up-sampler with an up-sampling factor
L, where L is a positive integer, develops an
output sequence xu [n] with a sampling rate
that is L times larger than that of the input
s

Spectral Analysis of Signals
1
Spectral Analysis of Signals
Spectral analysis is concerned with the
determination of frequency contents of a
continuous-time signal g a (t ) using DSP
methods
It involves the determination of either the
energy spectrum or

Additional Examples of Chapter 3: Discrete-Time Signals and Systems in the Frequency Domain
Example E3.1: Determine the DTFT X(e j ) of the causal sequence
where A, , o , and are real.
n
x[n] = A n cos(o n + )[n],
n e j0 n j e
Answer: x[n] = cos(o n + )[n

Additional Examples of Chapter 8:
Digital Filter Structures
Example E8.1: Determine by inspection whether or not the digital filter structure of Figure E8.1
has delay-free loops. Identify these loops if they exist. Develop an equivalent structure without

Additional Examples of Chapter 7: LTI Discrete-Time Systems in the Transform Domain
Example E7.1: Consider the following causal IIR transfer function:
H(z) = 3z3 + 2 z 2 + 5 (0.5z + 1)(z + z + 0.6)
2
.
Is H(z) a stable transfer function? If it is not stab

Additional Examples of Chapter 2: Discrete-Time Signals and Systems
Example E2.1: Analyze the block diagram of the LTI discrete-time system of Figure E2.1 and develop the relation between y[n] and x[n].
x[n]
+
_1
_ z 1
_ z 1
+ +
y[n]
d1
+
d2
Figure E2.1
A

Additional Examples of Chapter 10: FIR Digital Filter Design
Example E10.1: A lowpass FIR filter of order N = 65 and a transition band of width s p = 0.1 is to designed using the Parks-McClellan method. Determine the approximate values of the correspondin

Nirma University
Institute of Technology
Electronics and Communication Engineering Program
Class Test I September 2011
B. Tech. Semester V (EC)
2EC402: Digital Signal Processing
Date and time: 6/9/2012, 1 HOUR
Max. Marks: 30
NOTE: Attempt any 5 questions.