LTI Systems Flashcards
What is a Phasor?
A phasor is a complex number that encodes both the magnitude and phase of a sinusoidal signal.
How is a sinusoidal signal represented as a phasor?
A sinusoidal signal x(t) can be represented as a phasor X = Ae^jф.
What does A represent in the phasor representation?
A represents the amplitude (the peak value).
What does w represent in the phasor representation?
w represents the angular frequency of the signal.
What does ф represent in the phasor representation?
ф represents the phase shift of the sinusoid.
Fill in the blank: A phasor is the representation of a sinusoidal waveform in terms of its _______ and _______.
amplitude, phase
True or False: A phasor can only represent real numbers.
False
What formula is used to represent a phasor?
F=Aejθ
What form does a sinusoidal signal take?
x(t) = A cos(wt + ф)
What is the impulse response h(t) of a system?
The impulse response h(t) is the output of the system when the input is an impulse function d(t). It completely characterizes a Linear Time-Invariant (LTI) system.
How is the output y(t) related to the input x(t) in an LTI system?
The output y(t) is the convolution of the input x(t) with the impulse response h(t):
y(t) = (x * h)(t) = ∫ x(τ)h(t - τ) dτ
How does the frequency response H(jω) relate to the impulse response h(t)?
The frequency response H(jω) is the Fourier Transform of the impulse response h(t). It describes how the system modifies the amplitude and phase of different frequency components of the input signal.
What is the relationship between X(jω) and Y(jω) in an LTI system?
For an LTI system, the output in the frequency domain is the product of the input and the system’s frequency response:
Y(jω) = X(jω)H(jω)
What is convolution?
A mathematical operation that expresses the output of an LTI system as the integral or sum for discrete signals of the input signal x(t) or x[n] and the systems impulse response h(t) or h[n]
How does convolution relate to the fourrier transform in LTI systems?
Convolution in the time domain corresponds to multiplication in the frequency domain
