Chapter 10 Multiple choice questions

. Download the data file for the multiple-choice questions for Chapter 10, and open it in R. The file contains two vectors called HBwaveform and HBenvelope. They are from a 10-second audio recording of a fetal heartbeat, sampled at 44100Hz. Plot the waveform as a line plot and count the beats (note that there is some high frequency noise, but the beats are clear as bursts of activity). How many heartbeats are present?

9

11

15

20

. Calculate the Fourier transform of Hbenvelope, and plot the amplitude spectrum from 0-5Hz. Note that the sample is 10 seconds long. Aside from the DC component (at 0Hz), which frequency produces the largest amplitude?

0.5Hz

1Hz

1.1Hz

2.1Hz

. In the Fourier transform of the envelope, implement a crude low-pass filter by setting the amplitude of all frequencies above 5Hz to zero, then take the inverse transform. Do the same for the waveform. Plot both of the filtered signals. What do you observe?

The envelope still has clear peaks for each heartbeat, but the waveform does not.

The waveform still has clear peaks for each heartbeat, but the envelope does not.

The signals are smoothed, and both still have visible heartbeats.

Neither signal has a visible heartbeat.

. At the sample rate of 44100Hz, what is the Nyquist limit (the highest frequency we can represent)?

441000Hz

0.1Hz

44100Hz

22050Hz

. If we had a longer sample with a duration of 20 seconds, that was sampled at 260Hz, what would the frequency resolution of the Fourier spectrum be?

0.1Hz

0.2Hz

0.05Hz

20Hz

. The vector filter1 contains a filter in the temporal domain. Take the Fourier transform of the filter and plot the spectrum. The filter is:

A low pass filter

A bandpass filter

A high pass filter

A notch filter targeting a single frequency

. The matrix spatfilt contains the Fourier spectrum of a spatial filter. Plot the filter using the rasterImage function:
plot(x=NULL,y=NULL,xlim=c(0,1),ylim=c(0,1),axes=FALSE, ann=FALSE, lwd=2) rasterImage(spatfilt,0,0,1,1)
What can you deduce about its characteristics?

It allows through vertical information in a restricted frequency range

It allows through vertical information of all frequencies

It allows through horizontal information in a restricted frequency range

It allows through horizontal information of all frequencies

. The matrix ampspec contains the Fourier amplitude spectrum of an image. Based on the knowledge that the lowest spatial frequencies have the highest amplitudes in most images, where are these represented in this spectrum?

In the centre of the spectrum (i.e. the spectrum has been quadrant shifted)

In the corners of the spectrum (i.e. the spectrum has not been quadrant shifted)

At random around the spectrum

It depends on the phase spectrum, which has been removed

. The matrix filteredim contains an image that has been filtered. Display it using the rasterImage function. What sort of filter has been used?

A low pass filter

A high pass filter

A horizontally oriented filter

An obliquely (diagonally) oriented filter

. The matrix imspec contains the Fourier spectrum of a greyscale image. Note that the quadrants have not been shifted, so the lowest frequencies appear in the corners. Take the inverse transform of the matrix and display it as an image (you will need to scale the luminances between 0 and 1). What does it show?

A chicken

A rainbow

A mushroom

A cat

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