c sensor in a control system generates a signal with the frequency spectrum shown in Figure $7.$ The signal is filtered to give the output shown in Figure $8.$ Draw the idealised frequency response of the filter used and give estimated values of cut$-$off frequencies where possible. A hand drawn sketch is acceptable.

d What impact would increasing the number of taps in a digital filter design have on the width of the transition zone? What trade$-$off in the filter performance might be introduced by increasing the number of taps?

Frequency Spectrum

Figure $7$ Frequency spectrum of sensor signal

i$.$Figure $9$ shows two images of pictures from The Higgins Gallery, Bedford, UK$.$

Briefly say what the histograms show, and state which histogram belongs to which image. Justify your answer.

ii$.$Figure $10($a$-$b$)$ shows images of St$.$ Paul$$s Church in Bedford, UK$.$ The image in $($b$)$ is obtained by processing image $($a$)$ in VisionLab. Figure $10($c$)$ and $($d$)$ show colour histograms associated with the pictures in $($a$)$ and $($b$),$ but which set of histograms goes with which image is for you to establish by answering the following.

Summarise how the distribution of blue pixels in the histogram in $($d$)$ differs from that in the blue histogram in $($c$).$

What image processing technique is suggested by the difference the in the pixel distributions in the two blue histograms? Hence explain which set of histograms goes with image $($a$)$ and which with image $($b$)$

f$.$Figure $11($a$)$ shows a banner flag made up of a cyan $$H$$ letter on a white background. The histograms for the image are shown in Figure $11($c$).$

As shown in Figure $11($c$),$ the threshold values are set to Tred $=225,$ and Tblue $=200.$ Let the red greyscale of a pixel be denoted by r$,$ the green greyscale be denoted by g$,$ and the blue greyscale be denoted by b$.$

i$.$Say what would be seen if the image were thresholded so that all pixels with r $$ Tred $(225),$ g $$ Tgreen $(175)$ and b $$ Tblue $(200)$ become magenta. Give a screenshot to illustrate your answer.

ii$.$Say what would be seen if the image were thresholded so that all pixels with r $>$ Tred $(225),$ g $>$ Tgreen $(175)$ and b $>$ Tblue $(200)$ become yellow. Give a screenshot to illustrate your answer.

iii.It is required to segment this image to recognise the letter H on the banner flag. This is to be achieved by drawing a green box around the letter H as shown in Figure $11($b$).($Small green boxes outside the H in Figure $11($b$)$ can be ignored.$)$ Say which segmentation approach you would choose. Give a screenshot to illustrate your answer.

$($a$)$

$($b$)$

$($c$)($a$)$

$($b$)$

Green

threshold: $175$

Intensity $0-255$

Highchartsicom

threshold: $200$

Blue

Greyscale

Fiaure $11$ Image of a banner flag and its arevscale histoarams