The roots of this equation enable you to determine the stability of a digital filter.
What is the characteristic equation?
100
The DTFT of this function is equal to a constant value.
What is an impulse function?
100
A signal can always be represented by a weighted and shifted summation of these types of functions.
What are impulse functions?
100
This is the product of the complex conjugates
What is the complex conjugate of the product or what is the magnitude squared?
100
This is what happens when a continuous time sinusoidal signal is sampled at a rate that is less than twice the frequency of the sinusoidal signal.
What is aliasing?
200
As long as the coefficients of the difference equation for this type of digital filter are bounded, the filter will be stable.
What is an FIR filter?
200
These are the values at which the DTFT of the impulse response function goes to infinity.
What are the poles of the transfer function?
200
This is the output of a time invariant system when the input is equal to 1, only for n = 0, and the input is equal to 0 otherwise.
What is an impulse response function, h(n)?
200
In this form of Euler's identity, a 1/2 unit length complex phasor is rotating in the complex plane counter-clockwise and starts on the imaginary axis, and is added to another 1/2 unit length complex phasor with unit length starting just opposite on the imaginary axis, rotating clockwise at the same angular rate.
What is sin(w) ?
200
This rate at which frequencies greater than this are aliased back to lower frequencies.
What is the Nyquist Rate?
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
This is the period of the DTFT.
What is 2 pi?
300
These three mathematical algebraic properties hold true for convolution.
What are the associative, commutative, and distributive properties?
300
The real part of this function is equal to cos(w).
What is exp(jw) ?
300
This value of the independent variable "t" is used to find the value of the sequence at the index n for a sampled signal with sampling period equal to Ts.
What is t = nTs?
400
These properties of an FIR filters can be advantages in signal processing applications.
What are stability and linear phase?
400
The DTFT of this sequence is multiplied by exp(-jwN)
What is a sequence that is shifted by N indices?
400
This is the resulting DTFT operation based on the convolution between two sequences.
What is multiplication in the frequency domain.
400
This form of representing a complex number is equivalent the complex exponential form, A*exp(jw + phi).
What is the phasor representation?
400
This tonal effect due to aliasing can be heard when the frequency of a sampled sinusoidal signal is greater than the Nyquist rate.
What is frequency fold-back?
500
These are often used as the basic building blocks when desgining higher order IIR filters.
What are Second order Sections?
500
This form of signal representation consists of a weighted sum of complex sinusoidal functions.
What is the DTFT or what is the Fourier transform.
500
Another description of the output of an LTI system that is in terms of the impulse response function for that system.
What is a weighted sum of shifted impulses response functions?
500
This trigonometric identity taught in many high schools is more easily proven using Euler's Identity with exp(jx)*exp(-jx)=1.
What is cos(x)^2 + sin(x)^2 = 1 ?
500
The DTFT of this class of sampled continuous time signal is always an impulse at w=0, regardless of the sampling rate.