Final Flashcards
All continuous time signals can be completely represented by discrete time signals.
False
Aliasing occurs when the sampling frequency is less than two times the highest frequency in the continuous time signal.
True
Fitting a continuous time signal to a set of discrete samples is known as hybridization.
False
interpolation, reconstruction
Let xc(t) be a continuous time signal bandlimited to 2pi(1000).
Which sampling period T results in discrete samples x[n] = xc(nT) that capture all of the information in the original continuous time signal?
A: T = 1/1000
B: T = 2000
C: T = 1/500
D: T = 1/3000
D: T = 1/3000
2pi/T > 2(2pi(1000))
Cos(x) is equal to
(1/2)e^(jx) + (1/2)e^(-jx)
Dividing the time axis by T corresponds to multiplying the frequency axis by T.
True
If there is no aliasing and the discrete-time system is a lowpass filter, then the overall continuous time system will be a highpass filter.
False
Will be a lowpass filter as well.
Changing the sampling period T will change the overall continuous time filter frequency response Hc(jw).
True
If there is no aliasing a system will be capable of acting like an LTI system as long as the discrete time system Hd(e^(jΩ)) is LTI
True
Sin(x) is equal to
(1/(2j))e^(jx) - (1/(2j))e^(-jx)
Which of the following elements is NOT required to construct a block diagram of a linear constant coefficient difference equation.
A. Scaling a signal by a constant
B. Taking the derivative of a signal
C. Delaying a signal by one sample
D. Adding two signals
B. Taking the derivative of a signal
The frequency response generally increases in the region of the unit circle close to a pole, and decreases close to a zero.
True
How do you count the order of a block diagram of a linear constant coefficient difference equation?
Count the number of delays (i.e. z^-1)
Series combination looks like two systems getting combined together like a train in a block diagram of a linear constant coefficient difference equation,
True
The Discrete Fourier Transform X[k] is the derivative of X(e^(jw)) with respect to w.
False
Not the derivative but samples
One common use of the Discrete Fourier Transform is to approximate the Discrete Time Fourier Transform X(e^(jw)) for finite length data measurements.
True
Sampling in the frequency domain corresponds to making periodic copies in the time domain.
True.
To avoid aliasing in time, the DFT size N must be less than the length of the time domain signal x[n], M.
False
Not less than but > or equal to.
Buck has forgotten to upload 3 Whiteboards worth of content for this set.
True
Garret still doesn’t have the ability to upload images to Brainscape; thus he rephrased 2 questions that will give you the right idea when you see the problem on the exam.
True
The z-transform of x[n-1] is z^-1X(z)
True
The second order system
H(z) = 1 / (1 - (2rcos(θ)) z^-1 + r^2 z^-2)
will have peaks in the frequency response magnitude |H(e^jω)| near ω = ± θ
True
Convolving in time corresponds to adding z-transforms, so if
y[n] = x[n]*h[n]
then
Y(z) = X(z)+H(z)
False
Y(z) = X(z) x H(z)
Convolution in time <-> Multiplication in frequency
If an LTI system is causal and stable, then the system function H(z) must have all of its poles inside the unit circle.
True
