Lecture 18: Exam ReviewAnnouncementsWhat will the exam cover?What will the questions be like?More on the exam…Digital signal = a collection of numbersNumbers are easy to manipulate!Frequency content of signalsVarying Frequency ContentAnalog-to-Digital ConversionAliasingFilteringExamples of FilteringCompressionWatermarking, etc.Error CodingLecture 18: Exam ReviewThe Digital World of MultimediaProf. Mari OstendorfEE299 Lecture 1820 February 2007Announcements HW5 due today, Lab5 due next week Lab4: Printer should be working soon….  Exam: Friday, Feb 22 Review in class today Sample exam solutions posted tonight Note: previous exam did not cover error coding or watermarking, but this year’s might Ostendorf office hours: Thurs 1:30-3 Fri 9:30-12EE299 Lecture 1820 February 2007What will the exam cover? Key concepts in the class so far… Digital signal = a vector/matrix of numbers Frequency content of signals Analog-to-digital: sampling & quantization Filtering Compression Watermarking, error coding…for both sounds and images (gray & color) Material in lectures, labs, HWMore on each topic to come!EE299 Lecture 1820 February 2007What will the questions be like? Similar to homework and quizzes Multiple question types: conceptual (e.g. what type of filter is the floor of your apartment?) pictorial (which image has more high frequency content?), possibly audio something involving equations simple calculations (sample rate, compression factor, bits/image,…); calculators not required simple MATLAB commands (see sample exam)EE299 Lecture 1820 February 2007More on the exam… No calculators, cell phones, etc. Open notes (but you are advised to have a summary sheet); no books Exam starts and ends promptly Be sure to JUSTIFY YOUR ANSWERS! No credit for no work (e.g. one word answers) Partial credit for reasonable justification even if the answer is wrongEE299 Lecture 1820 February 2007Digital signal = a collection of numbers Time signal (speech, audio, bird sounds, …)Vector: X(n) n=1,…,T  Grayscale imageMatrix: X(i,j) i=1,…,M j=1,…,N Color imageMatrix x 3: X(i,j,k) i=1,…,M j=1,…,N k=1,2,3(one matrix each for R, G & B)EE299 Lecture 1820 February 2007Numbers are easy to manipulate! Signals are can be generated from… Weighted sums of sinusoids (or other base signals) Concatenating different signals Math operations can change signals: Mixing (Z=aX+bY) Envelope scaling (Z=XY) Echo/shadow Z=X + aXshifted Time reversal (Z(n)=X(N-n))(same idea works for mirror images) Filtering (see subsequent slide)EE299 Lecture 1820 February 2007Frequency content of signals Audio signal ImageEE299 Lecture 1820 February 2007Varying Frequency Content Audio signal: spectrogram (time slices)  Image: Block DCT (space blocks)EE299 Lecture 1820 February 2007Analog-to-Digital Conversion Two key steps: Time/space sampling Amplitude quantization Very important concept: aliasing Shannon’s sampling theorem for time signals: sampling rate Fs > 2Bwhere B=bandwidth of analog signal to be sampled When Fs<2B, you get aliasing: high frequencies sound/appear lower, mix with actual low frequencies  Same basic idea holds for imagesEE299 Lecture 1820 February 2007Aliasing Time Signals Fs=samples per second Images Pixels per inchdownsampleSingle tone sounds lower frequencySinging or speech sounds muffledEE299 Lecture 1820 February 2007Filtering Linear scaling of the frequency content of signals Important types of filters:  Low pass filter:  Mainly low frequencies left Smoothing effect, blurring for images High pass filter:  Mainly high frequencies left Emphasizes noise (speckles in an image), highlights edges or abrupt changes Can build other filters from these two Bandpass filter: keep middle frequencies only Bandstop filter: keep high and low, but not middleEE299 Lecture 1820 February 2007Examples of Filtering Sound signals ImagesoriginalfilteredfilteredoriginalEE299 Lecture 1820 February 2007Compression General steps Two types of compression Lossless:  No change to sound/image when recovered Takes advantage of redundancy & imbalanced distributions Examples: entropy coding, run-length coding  Lossy Some changes to the sound/image, hopefully subtle Takes advantage of human perception (esp. frequency domain) Examples: MP3 (audio files), JPEG (images)Compress/EncodeDecompress/DecodeStorageorCommunicationfastersmallerCost: more computingWhy compress?EE299 Lecture 1820 February 2007Watermarking, etc. Embed a low bit rate signal in a high bit rate signal (i.e. not fully compressed) Invisible watermarking (or information hiding) takes advantage of the same perception tricks as compression ADDS bits to signal compared to compression (replace vs. omit low order bits) Issues: robustness, security, ….EE299 Lecture 1820 February 2007Error Coding ADD bits to the signal to help detect and sometimes correct errors Examples: Parity code (detection only) Repetition code (correct errors by majority