ECE-5200
Introduction to Digital Signal Processing
Autumn 2014
Homework #7
Oct. 24, 2012
HOMEWORK SOLUTIONS #7
1. For this, we can use the DFT denition plus a variable change (m = N 1 n):
N 1
N 1
Y [k]
2
2
x[N 1 n]ej N kn
y[n]ej N kn =
=
n=0
n=0
N 1
N 1
2
ECE-5200
Introduction to Digital Signal Processing
Homework #1
Autumn 2012
Aug. 22, 2012
HOMEWORK ASSIGNMENT #1
Due Wed. Aug. 29, 2012 (in class)
Problems:
1. Consider a discrete-time system H whose output, given input cfw_x[n] , is given by y [n] =
n=
2
ECE-5200
Introduction to Digital Signal Processing
Au14
Midterm #1
Oct. 10, 2014
MIDTERM #1 SOLUTIONS
1
1. (a) Recalling the correspondence T = 12 = 2, we have that 8
Then, recalling that the DTFT is 2-periodic, we get
4
3
and 16
8
3 .
|X(ej )|
12
2
4
ECE-5200
Introduction to Digital Signal Processing
Spring 2013
Homework #4
Feb. 1, 2013
HOMEWORK ASSIGNMENT #4
Due Fri. Feb. 8, 2013 (in class)
Problems:
1. Consider the continuous time signal
x(t) =
sin(0.2t)
.
t
(a) Find and sketch the CTFT of x(t), cal
ECE-600
Introduction to Digital Signal Processing
Homework #2
Autumn 2012
Aug. 29, 2012
HOMEWORK ASSIGNMENT #2
Due Fri. Sep. 7, 2012 (in class)
1. Evaluate the following integrals and sums, using a case statement to express your answers when
needed (e.g.,
ECE-5200
Introduction to Digital Signal Processing
Autumn 2012
Homework #1
Aug. 27, 2012
HOMEWORK SOLUTIONS #1
1. Here, the input/output relationship of H is y [n] =
2
m=0
x[n m] = x[n] + x[n 1] + x[n 2].
(a) For H to be linear, we need that
Hcfw_x[n] + w
ECE-5200
Introduction to Digital Signal Processing
Midterm #2
Au14
Nov. 21, 2014
MIDTERM #2 SOLUTIONS
1. Recalling that x=[1,2,3] and h=[2,1,-1], we have the following.
(a) ifft(fft(x,3).*fft(h,3) = [3,2,7] since this is equivalent to a 3-circular convolu
ECE-5200
Introduction to Digital Signal Processing
Practice Midterm #2
Au14
Nov. 20, 2014
PRACTICE MIDTERM #2 SOLUTIONS
1. Recalling that x=[1,3,2] and h=[1,-1,2], we have the following.
(a) conv(x,h) = [1,2,1,4,4] since:
1
3
2
2 1
1
2 1
1
2 1
1
2 1
1
2 1
ECE5200
Issued: March 6, 2015
Assignment # 7
Due: March 13, 2015
Current Reading: Lecture packets #3 & #4; associated text chapters.
1 FFT
(a) Which of the following Fast Fourier Transforms would require more computation?
(i) > fft(x,139)
(ii) > fft(x,256
ECE-5200
Introduction to Digital Signal Processing
Homework #4
Fall 2013
Sep. 17, 2013
HOMEWORK ASSIGNMENT #3
Due Wed. Sep. 25, 2013 (in class)
Problems:
1. Suppose that a real continuous time signal, w(t), has CTFT given by the diagram below. For each
|W
ECE 5200 Assignment #7 Solutions & Comments Spring 2015
1. FFT
(a) The command fft(x,256) requires less computation than fft(x,139), even though more
frequency samples are computed.
Since 139 is a prime number (factor(139) tells you that its only factor i
ECE 5200 Assignment #4 Solutions & Comments
Spring 2015
1. The sampling interval is T = 0.01. The sampled input signal is
x[n] = x(t) |t=nT = cos(2385n/T + /3) = cos(7.7n + /3)
Thus, the frequency, in radians per sample, of the discrete-time cosine signal
ECE-5200
Introduction to Digital Signal Processing
Midterm #1
Sp14
Feb. 18, 2014
MIDTERM #1 SOLUTIONS
1. (a) Recall that the IDTFT of a unit-height rectangle spanning the interval [0 , 0 ) equals
sin(0 n)/(n), which has height 0 / and nulls at k/0 for int
ECE5200
Issued: February 27, 2015
Assignment # 6
Due: March 6, 2015
Current Reading: O&S text: DFT chapter; lecture packet #3.
1 Circular convolution
Let x = [1, 2, 3] and h = [2, 1, 4].
(a) Find the convolution of x and h.
(b) Find the circular convoluti
ECE 5200
Lori Dalton
January 7, 2013
Introduction:
Much of modern engineering is concerned with signals
and systems.
A signal is an information-containing waveform
(e.g., audio signal, image, digital video stream)
A system converts one waveform to anot
ECE-5200
Introduction to Digital Signal Processing
Autumn 2017
Homework #4
Sep. 15, 2017
HOMEWORK ASSIGNMENT #4
Due Fri. Sep. 22, 2017 (in class)
1. Consider the conjugated sampler that gives x[n] = x (nT ). Express X(ej ), the DTFT of x[n]
in terms of Xc
The Ohio State University
Department of Electrical & Computer Engineering
ECE 5200 INTRODUCTION TO DIGITAL SIGNAL PROCESSING Sp2015
Instructor:
Lee C. Potter, 716 Dreese Labs, [email protected]
E-Access:
http:/carmen.osu.edu
Oce Hours:
Mon 4:305:20pm (DL7
FIR Example
y[n] = 0.5x[n] + x[n 1] + 0.5x[n 2]
This is a second-order FIR lter, and hence is a linear time-invariant system.
We have that
h[n] = 0.5[n] + [n 1] + 0.5[n 2]
To nd H(ej ), we start with the denition
H(ej ) =
h[k]ejk
k=
1 0
1 j2
j
= e + 1e
+
ECE-5200
Introduction to Digital Signal Processing
Homework #6
Autumn 2017
Oct. 6, 2017
HOMEWORK ASSIGNMENT #6
Due Fri. Oct. 13, 2017 (in class)
1. Consider two sequences: x = [1, 2, 3] and w = [1, 2, 3, 4].
(a) Compute the linear convolution of these seq
ECE-5200
Introduction to Digital Signal Processing
Autumn 2017
Practice Midterm #1
Oct. 5, 2017
PRACTICE MIDTERM #1 SOLUTIONS
1. (a) Recalling the correspondence T1 = 12 = 2, we have 3
recalling that the DTFT is 2-periodic, we get
2
and 5
5
6 .
Then,
5
Introduction:
Much of modern engineering is concerned with signals
and systems.
Roughly, a signal is an information-containing waveform
(e.g., audio signal, image, digital video stream) and a
system converts one waveform to another (e.g., low pass
lter,
Sampling and Reconstruction:
Until now, we have considered continuous-time signals &
systems separately from discrete-time signals & systems.
We will now connect them through uniform sampling :
x[n] = x(nT ) for n Z,
where T (in seconds/sample) is the s
F229 Ca
Sampling DTFT/CTFT relationship (c nt):
hwwmcccéx
In words, the e uation
says that the DTFT spectrum X(ejw) is composed of
o amplitudescwangd (by factor f3 ggfig
o frquemgwgygstretched (by factor T), and
o 27TkShlf
%2§MM
g 152). These
The Ohio State University
Department of Electrical and Computer Engineering
ECE 5200 INTRODUCTION TO DIGITAL SIGNAL PROCESSING Au17
Instructor:
Prof. Phil Schniter, 616 Dreese Labs, [email protected]
E-Access:
http:/carmen.osu.edu
Office Hours:
TBD. (Out
ECE-5200
Introduction to Digital Signal Processing
Au17
Midterm #1
Oct. 6, 2017
MIDTERM #1 SOLUTIONS
1. (a) Recalling the correspondence T1 = 4 = 2, we have that 5 5
2 = 2.5 and
9
9 2 = 4.5. Then, recalling that the DTFT is 2-periodic, we get
|X(ej )|
4
2
ECE-5200
Introduction to Digital Signal Processing
Autumn 2017
Practice Midterm #1
Oct. 5, 2017
PRACTICE MIDTERM EXAMINATION #1
Name:
Instructions:
Do not turn over this cover page until instructed to do so.
You will have 48 minutes to complete this exa