IT2035
Laboratory Exercise
System Response
Basic Principles:
The frequency response of a Discrete-Time system is something experimentally measurable and something
that is a complete description of s linear, time-invariant system in the same way that the impulse response is.
The frequency response of a linear, time-invariant system is defined as the magnitude and phase of the
sinusoidal output of the system with a sinusoidal input.
More precisely, if
𝒙(𝒏) = 𝒄𝒐�(𝑚𝒏) and the output of the system is expressed as
𝒚(𝒏) = 𝑴(𝑚)𝒄𝒐�(𝑚𝒏 + 𝝋(𝑚)) + 𝑻(𝒏)
where T(n) contains no components at ω, then M(ω) is called the magnitude frequency response and φ(ω) is
called the phase frequency response. If the system is causal, linear, time-invariant, and stable, T(n) will
approach zero as n→∞ and the only output will be the pure sinusoid at the same frequency as the input. This
is because a sinusoid is a special case of zn and, therefore, an eigenvector.
The response of a discrete-time system to a unit sample sequence (n) is called the unit sample response or
impulse response h(n)
The response of a discrete-time system to a unit step sequence u(n) is called the unit step response or step
response s(n).
Procedure:
1. Given the difference equation y(n) = 2x(n) – 3x(n-1) + 5x(n-2) + 2y(n-1) -7y(n-2), get the system transfer
function using the following procedure:
Group similar terms y(n) -2y(n-1) +7y(n-2) = 2x(n) +3x(n-1) +5x(n-2)
Get the z transform of the equation y(z) – 2z -1y(z) + 7z-2y(z) = 2x(z) + 3z-
1
x(z) +5z-2x(z)
Group using the common factor
y(z)(1 – 2z-1 + 7z-2) = x(z)(2 + 3z-1 +5z-2)
Get h(z) = Y(z) / X(z)
System transfer function is
03 Laboratory Exercise 1 *Property of STI
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Laboratory Exercise
System Response
Basic Principles:
The frequency response of a Discrete-Time system is something experimentally measurable and something
that is a complete description of s linear, time-invariant system in the same way that the impulse response is.
The frequency response of a linear, time-invariant system is defined as the magnitude and phase of the
sinusoidal output of the system with a sinusoidal input.
More precisely, if
𝒙(𝒏) = 𝒄𝒐�(𝑚𝒏) and the output of the system is expressed as
𝒚(𝒏) = 𝑴(𝑚)𝒄𝒐�(𝑚𝒏 + 𝝋(𝑚)) + 𝑻(𝒏)
where T(n) contains no components at ω, then M(ω) is called the magnitude frequency response and φ(ω) is
called the phase frequency response. If the system is causal, linear, time-invariant, and stable, T(n) will
approach zero as n→∞ and the only output will be the pure sinusoid at the same frequency as the input. This
is because a sinusoid is a special case of zn and, therefore, an eigenvector.
The response of a discrete-time system to a unit sample sequence (n) is called the unit sample response or
impulse response h(n)
The response of a discrete-time system to a unit step sequence u(n) is called the unit step response or step
response s(n).
Procedure:
1. Given the difference equation y(n) = 2x(n) – 3x(n-1) + 5x(n-2) + 2y(n-1) -7y(n-2), get the system transfer
function using the following procedure:
Group similar terms y(n) -2y(n-1) +7y(n-2) = 2x(n) +3x(n-1) +5x(n-2)
Get the z transform of the equation y(z) – 2z -1y(z) + 7z-2y(z) = 2x(z) + 3z-
1
x(z) +5z-2x(z)
Group using the common factor
y(z)(1 – 2z-1 + 7z-2) = x(z)(2 + 3z-1 +5z-2)
Get h(z) = Y(z) / X(z)
System transfer function is
03 Laboratory Exercise 1 *Property of STI
This study source was downloaded by 100000899610689 from CourseHero.com on 09-24-2025 09:11:14 GMT -05:00 Page 1 of 3
https://www.coursehero.com/file/153589644/03-Laboratory-Exercise-17-DSPdocx/
