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Tell me the difference
Down to Funky Town (DTFT)
Would you like a sample?
Euler you fool!
Systems, systems, and more systems
100
The location of these quantities enable you to determine the stability of a digital filter.
What are poles?
100
The DTFT of this function is a constant value.
What is an impulse function?
100
This effect occurs when a continuous time sinusoidal signal is sampled at a rate less than twice its frequency.
What is aliasing?
100
The magnitude of exp(jw) is always this value, regardless of w.
What is 1?
100
An output of an LTI system due to a sinusoidal input will be the same sinusoidal signal modified by this quantity.
What is the frequency response of the system (evaluated at that particular frequency)?
200
As long as the coefficients of the difference equation for this type of filter are bounded, the filter will be stable.
What is an FIR filter?
200
The DTFT "lives" on this region of the complex z-plane.
What is the unit circle?
200
This value of the continuous time independent variable "t" is used to find the value of the corresponding sampled sequence at index "n".
What is nTs (where Ts is the sampling period)?
200
This trigonometric function gives the imaginary part of a complex exponential exp(jw).
What is sin(w)?
200
This the output of a linear time-invariant system when the input is 1 at time 0, and 0 at all other times.
What is the impulse response, h(n)?
300
Typically, this type of digital filter requires a lower order to meet the same stop and pass band specifications.
What is an IIR filter?
300
The DTFT is always periodic in frequency, with this fundamental period.
What is 2pi?
300
The DTFT of this sampled signal is always an impulse at w=0, regardless of the sampling rate.
What is a constant?
300
The equivalent of "-j" written in complex exponential form.
What is exp(-j pi/2)?
300
This frequency domain operation is the equivalent of convolution in the time domain.
What is multiplication?
400
This property of all FIR filters can be advantageous in many signal processing applications.
What is linear phase?
400
This time-domain operation results in multiplication by exp(-jwN) in the frequency domain.
What is a sequence shift by N indices?
400
This transform is a sampled version of the DTFT.
What is the DFT?
400
The complex exponential exp(jw) is always periodic in w with this period.
What is 2pi?
400
A cascade of LTI systems having impulse responses h1(n) and h2(n) have this equivalent impulse response.
What is h1(n) convolved with h2(n)?
500
These are used as building blocks when implementing high order IIR filters.
What are bi-quads (or second order sections)?
500
The DTFT of a real-valued sequence always exhibit this symmetry in the frequency domain.
What is conjugate symmetry?
500
This frequency is produced when samples of a 1000Hz sinusoidal signal sampled at 1200Hz are reconstructed using an ideal reconstruction filter.
What is 200Hz?
500
This trigonometric identity, often taught in high school, is more easily proven using Euler's Identity with exp(jx)*exp(-jx)=1.
What is cos(x)^2 + sin(x)^2 = 1?
500
These mathematical functions are eigen-functions of LTI systems.
What are complex exponentials?