Question

The impulse response of a filter is the following: h[n] = u[n].

Is it an FIR filter or and IIR filter. Explain

Answer #1

Given filter is IIR filter.

In order to solve this problem we need to know about FIR and IIR filters...

**FIR** means Finite Impulse Response.It means
Impulse response of filter should be countable or Finite in
nature...

FIR filters are always stable

**IIR** means Infinite Impulse Response.As the
definition itself says impulse response of this filter is Infinite
in nature.

IIR filters may or may not be stable.

Our filter impulse response is unit step which is Infinite.

Step function is not finite.And from the stability criteria also Unit step is unstable.

From all the above , we can conclude that our filter is
**** not FIR, it's an IIR filter.

**Finally , filter whose impulse response is unit step is
an IIR filter.**

If you have any doubt ask in comment...

If you like the answer give thumps up...

Thank you...

****

Prove that the amplitude response of an FIR filter H(z) of order
N with real coefficients h[n] has symmetry.

An LTI discrete-time system has the impulse response h[n] =
(1.2)^n * u[-n]. Find the system response to a unit step input x[n]
= u[n].
Please explain the shifting im having a hard time grasping the
concept (especially for the U[-n+k] shift
Note:u[n] is the unit step function

Given an input signal x[n], and the impulse response h[n],
compute the output signal.
x[n] = a^n *
u[1-n] for
|a| > 1
h[n] = u[2-n]

Classify each of the following as
either true or false.
(a) In the FIR design using the window
method, side lobes appear due to numerical round-
off
errors
(b) The DC gain of the transfer
function H(z) = is 0.4
FIR Filters have all zeros at the origin.
IIR (recursive) Filters can never be unstable
Windows are used in FIR Filter design to reduce the size of
side lobes in the frequency response.
A causal Filter will always have a...

PLEASE ANSWER QUESTION #2
Design an FIR band-pass filter with cutoff frequencies of π/ 4
and π/ 6 . The filter’s impulse response should have 81 samples
(i.e. N = 81). Use a Blackman filter window.
(a) Plot the filter’s impulse response
(b) Plot the magnitude of the filter’s frequency response, in
dB. (i.e. 20 log(|H(e jω)|))
(c) Print out the MATLAB code used in the filter design
2. Use the filter designed in #1 to filter a random input...

A linear time invariant system has an impulse response given by
ℎ[?] = 2(−0.5) ? ?[?] − 3(0.5) 2? ?[?] where u[n] is the unit step
function.
a) Find the z-domain transfer function ?(?).
b) Draw pole-zero plot of the system and indicate the region of
convergence.
c) Is the system stable? Explain.
d) Is the system causal? Explain.
e) Find the unit step response ?[?] of the system, that is, the
response to the unit step input.
f) Provide...

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Justify.

An LTI system has an impulse answer of h[n] = a^(n)H[n], H[n] is
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defined by> y[n] - ay[n-1] =x[n] Find the output when the input
is x[n] = Kb^(n)H[n], and y[-1]=y_(-1)\ Find the output when the
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consider the discreter time system y[n]=3x[n-1] +4x[n].this FIR
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A continuous-time system with impulse response
h(t)=8(u(t-1)-u(t-9))
is excited by the signal
x(t)=3(u(t-3)-u(t-7))
and the system response is y(t).
Find the value of y(10).

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