Chapter 4: Signal Representation using Fourier Series
Problem 4.1
(a)
Using Definition 4.4, the CT function x1(t) can be represented as x1(t) = c11(t) + c22(t) + c33(t)
with the coefficients cn, for n = 1,2, and 3, given by
T
c1 =
1
2T
x1 (t )1 (t )dt =
Chapter 3: Time Domain Analysis of LTIC Systems
Problem 3.1
Linearity: For x3(t) = x1(t) + x2(t) applied as the input, the output y3(t) is given by
d n y3
dt n
+ an 1
d n 1 y3
+
dt n 1
+ a1
dy3
d m 1 (x1 (t ) + x2 (t )
d m (x1 (t ) + x2 (t )
+ a0 y3 (t )
Chapter 1: Introduction to Signals
Problem 1.1:
i) z[m,n,k] is a three dimensional (3D) DT signal. The independent variables are given by m, n, and k,
while z is the dependent variable. Digital video is an example of a 3D DT signal of the form z[m,n,k]. T
Chapter 2: Introduction to Systems
Problem 2.1
(i)
The currents flowing out of node 1 along resistors R1, R2, and capacitor C, are given by
iR1 =
y (t ) v (t )
,
R1
iR 2 =
y (t )
,
R2
iC = C
dy
dt
Applying the Kirchoffs current law to node 1 and summing u