Chương 1:A video movie of 150 minutes duration is digitally represented in format ITU-R 601(720x576 pixels luminance, 2x360x576 pixels chrominances per frame, 25 frames/s, 8bit/pixel PCM).a) Which hard disc capacity is required to store the entire movie in ITU-R 601 encoding?b) The movie shall be encoded using MPEG-2 compression, achieving a compressionfactor of 40:lover PCM. Which file size is now required to store the stream on thehard disc?c) To transmit the movie over a satellite channel, error protection by channel coding isprovided . This increases the rate by 10 %. Which transmission bandwidth (Mbit/s) ofthe channel is necessary?Problem 1.2Images from a Web camera shall be transmitted over a telephone modem, providing aconstant data rate of 56 kbit/s. 16 kbit/s are needed for speech transmission. The frame rateshall be 10 frames/soa) As the video coder does not output a constant-rate stream, it is necessary to buffer theinformation before transmitting over the channel. What maximum buffer size (measuredin bits) is allowable, if the maximum delay caused by buffering shall be 200 ms?b) The output rate of the encoder can be changed by modification of the quantizer setting(the discrete-step 'Q factor'). As a rule of thumb, lowering the Q factor by one stepmay increase the rate by a factor 1.1. For one frame, it is measured that encoding hasconsumed 4.84 kbit. By how many steps must the Qfactor be lowered or increased toavoid an over-run or under-run ofthe buffer

Chương 2

The vectors a=[2 O]T and b=[2 I]T establish a basis system A=[ a b ].a) Determine the vectors of the dual basis A, such that the property ofbiorthogonality isfulfilled.b) Sketch the positions of all four vecto::, in a coordinate system.c) Compute the determinants ofA and A .

Problem 2.2a) Prove the condition for hexagonal sampling (2.62).b) What is the ratio of the area of the base band in Fig. 2.l3c (shaded), as compared tothe rectangular sampling case with OJR=OJS?c) What is the ratio of the horizontal sampling distance R in Fig. 2.12c, as compared tothe rectangular sampling case with R=8 ?d) Compute the determinant of the sampling matrix Dhe:n normalized by 8=1. Comparethe value against the results from parts b) and c).e) The CCD chip ofa digital camera has an active area of 10 mm x 7,5 mm. The numberof pixels is 4.000,000. Compute the approximate vertical sampling distances 8 for thecases ofrectangular sampling (R=S) and hexagonal sampling .Problem 2.3A two-dimensional cosine of horizontal frequency OJ,=OJs/3 is sampled by a quincunx grid(see Figs. 2.12d and 2.13d) .a) Determine the upper limit for vertical frequency OJz(absolute value) guaranteeing aliasfree sampling .b) Which horizontal frequency becomes visible after ideal lowpass filter reconstructionfrom the sampled signal, ifthe vertical frequency is OJz=OJs /3?Problem 2.4By motion of a video camera using progressive sampling, a translational motion shift ofk=20 pixels horizontally and 1=10 pixels vertically results . The frame rate is 50 frames/s,the CCD chip of the camera has a size of 10 mm x 7.5 mm, and the number of pixels is

360 x 288.a) Determine the horizontal and vertical velocities u and v, by which the points move onthe image plane.b) The camera shoots a cosine oscillation, where in the sampled image one period is 40pixels . Which is the maximum allowable frequency in horizontal direction, such thatthe sampling theorem is not violated , i.e. the motion of the camera can be interpretedcorrectly?

a) Determine a sampling matrix D.b) Compute the related frequency sampling matrix F.c) Which is the shape of the base band in the 3D frequency domain?Problem 2.6A 2D signal shall be sampled by the grid shown in Fig. 2.19, where the black and whitedots establish two rectangular sub-grids of equal sampling distances. The black grid isshifted horizontally and vertically by R' and S' relative to the white grid.

RFig. 2.19. Sampling grid composed by two rectangular sub-gridsa) For a given vertical sampling distance S, determine values of R, R' and S', such thati) a quincunx grid ii) a hexagonal grid results.b) Describe the sampling of signal x(r,s) by a sampling function ':>.o(r) which is a superpositionof two (black&white bullet) rectangular impulse grids ':>R.S.c) Determine the Fourier spectrum of ':>.o(r) . For which cases will the number ofperiodicspectral copies be lower than' for one of the rectangular-grid spectra?d) Values OSR.'~, OSS'SS shall be allowed. Under which conditions will it not be possibleto express the sampling function ':>.o(r) by a closed-form expression, using a samplingmatrix D?e) For R=S, R'=S'=S/2 sketch the spectrum of a signal, which was sampled observing the

sampling criteria (Sketched frequency layout shall at least include the base band and theeight nearest alias frequency bands).t) A signal xcCr,s) =A cos[ 27(/S (r+s) ] + B cos[ 27(/S (r-s) ] is sampled by the grid givenin e). Which signal will be observed after reconstruction using an ideal lowpass filterwith same pass band as the base-band shape?