BME 350- exam 4

passive filter

one that contains only R, L, and C components- It is not necessary that all three be present

active filter

one that, along with R, L, and C components, also contains components with a voltage source, e.g. OPAMP

poles and zeros can be

positive, negative or complex in general

sampling

measuring the value of an image at a finite number of points

Nyquist rate

2*Fmax

Minimum number of bits required per pixel to represent a grayscale image with at least 50 shades of grey

6

continuous FT

Decomposes a signal x(t) into complex sinusoids of the form e^jwt (basis functions with imaginary exponent)

discrete FT

Decomposes a signal x[n] into complex sinusoids of the form e^jw n

For Laplace transform, ROC consists of a circular strip or ring around origin in the z-plane

F

ROC contains at least one pole

F

nyquist frequency

F max = wm

aliasing can be prevented using

Nyquist rate

STABLE

ROC contains the unit circle (for z transform) or the imaginary axis (for Laplace)

For left handed x[n]

ROC is inside the inner most pole

Causal

ROC is outside the outermost pole (for z transform) or to the right of the right most pole (for Laplace)

For left handed x(t)

ROC is to the left of the left most pole

For discrete signals, frequency axis maps bandwidth range 0- 𝜔𝑚 to angles 0-π on the unit circle on the z-plane.

T

If the gain factor is given, one can deduce the transfer function from the location of poles and zeros

T

If the unit circle is within the ROC of a ZT H(z) of an impulse response h[n], then the FT H(w) converges and h[n] is absolutely summable.

T

In digital filter design, you can suppress a frequency ω0 by placing a zero at an angle W0 = ω0 π / ωm on the unit circle.

T

Laplace transform extends the concept of Fourier transform by using complex exponent s=σ+ jω instead of jω.

T

analog filters are generally implemented using hardware while digital filters are generally implemented using software

TRUE

band limited

a signal definitely does not havecomponents of frequency greater than a certain value, designated asω𝑀 and the graph of X (𝑗ω) is zero beyond ω𝑀

Each point in k-space represents

a spatial sinusoid of a certain frequency and amplitude and contributes to the whole image

A low pass filter

allows frequencies below a cutoff frequency

band pass filters

allows frequencies within a certain range and eliminates the rest

A high pass filter

attenuates frequencies below a cutoff frequency

ROC of X(s)

contains no poles

sampling

conversion of continuous signal to discrete signal

multiplication in the time domain

convolution in the frequency domain (and vice versa)

image size

determined by both the number of samples and bit resolution of quantization. May be also determined by additional "dimensionality"of captured image

DFT

discrete version of the DTFT

Laplace transform

extension of continuous Fourier transform

Z transfrom

extension of the discrete Fourier transform where e^(j*omega*n) is replaced with re^(j*omega*n)

In a magnitude bode plot the horizontal and vertical axis are :

frequency, magnitude in Db

outermost pole of H(z) lies inside the unit circle

h[n] represents a stable and causal system

for discrete signals

he frequency spectrum is equivalent to the magnitude of the transfer function H(z) evaluated on the UNIT CIRCLE

edge information

high frequency components in the k-space

The edge of the space represents

high frequency spatial sinusoids

poles near unit circle

indicate filter's passbands

DTFT is

intrinsically periodic in frequency

pole

is the value of s when D(s) is zero, denoted by X on the complex plane

zero

is the value of s when N(s)=0 , denoted by O on the complex plane

the center of the k space represents

low frequency spatial sinusoids

filtering

process of changing the relative amplitudes of the frequency components of a signal (e.g.eliminating or enhancing certain frequencies)

ideal sampling

produces samples equivalent to the instantaneous value of the continuous signal at the desired points

resolution

refers to the size of the pixels (e.g. 5x5 mm2 per pixel). A higher resolution means smaller pixels.

For two sided signal, ROC is

region inside or outside of poles

Images can be decomposed into a sum of

spatial sinusoids

ROC consists of a

strip parallel to jw in the s-plane

filter

system performing filtering

For finite duration, ROC is

the entire s plane

for continuous signals

the frequency spectrum is equivalent to the magnitude of the transfer function H(s) evaluated on the IMAGINARY AXIS

quantization

the representation of the measured value at the sampled point by an integer

For right handed x(t), ROC is

to the right of the right most pole

A computer represents an image

using binary integers in a process called quantization

kernel

what an impulse function(h) is referred to in image space