SSS response essentially characterizes the system function.
SSS response is commonly used to measure the system function.A common mode of thinking for signal processing tasks is “filtering.” All physical systems act as filters of their input signals. Filtering is an important signal processing method.
Lecture #11:
SINUSOIDAL STEADY-STATE (SSS) OR FREQUENCY RESPONSE
Motivation:
Many systems operate in the SSS, e.g., electrical power distribution, broadcast, touch-tone telephone.
SSS response essentially characterizes the system function.
SSS response is commonly used to measure the system function.
A common mode of thinking for signal processing tasks is “filtering.” All physical systems act as filters of their input signals. Filtering is an important signal processing method.
Outline:
Causal, stable systems
Sinusoidal steady-state response—the frequency response
Relation of frequency response to system function
Bode diagrams
Signal processing with filters
Lowpass and highpass filters
Resonance and bandpass filters
Notch filters
Conclusions
A system that operates in the SSS . . . well almost
The touch-tone phone
Dialing consists of pressing buttons on the keypad which has 3 columns and 4 rows. How is the information about which button is pushed coded?
Demo on coding in the touch-tone phone.
Sum of sinusoids
times a pulse window p(t)
More on the effect of p(t) later!
I. CAUSAL, STABLE SYSTEMS
The system function of an LTI system, H(s), can be used to categorize systems.
Causal system
ROC is to the right of the rightmost pole of H(s).
Causal, stable system
ROC is to the right of the rightmost pole of H(s) and all the poles are in the left-half of the s plane.
More on the definition of stable systems at a later time.
A causal, stable system has the pole-zero diagram shown below.
For s in the shaded region, the response to
is the steady-state response
II. THE SYSTEM FUNCTION H(S)
1/ Real and complex poles
H(s) is a complex function of a complex variable s. The plots show |H(s)|.
2/ Effect of a zero
3/ Interpretation of H(s) by pole and zero vectors
H(s) that is a rational function has the form
H(s) consists of products and quotients of the form
. Each of these terms are vectors in the complex s plane:
are called zero vectors,
are called pole vectors.
=
The vector
points from
to s. It can be expressed in polar form as