Lecture 4: From Analog to DigitalAnnouncementsPlan for TodaySignals in the Frequency DomainTwo Types of SignalsFrequency Content vs. TimeDemo: Seeing SoundWhich sound goes with which picture?Analog vs. DigitalSampling: A revolutionary concept!Things that we sample:Sampling a SinusoidAliasing for Video Signals (Wagon Wheel Effect)Hearing and Seeing AliasingLecture 4: From Analog to DigitalThe Digital World of MultimediaProf. Mari OstendorfReading: Orsak et al., Chapter 5EE299 Lecture 414 Jan 2008Announcements Assignments due this week:  Lab1 (Matlab intro) and HW1 (see course web page) Lab 2 assignment will be posted tonight, so you can start on that if you’ve finished Lab 1 Sieg 232 access: Any remaining access problems??EE299 Lecture 414 Jan 2008Plan for Today Review: Signals in the Frequency Domain Collaborative quiz SamplingEE299 Lecture 414 Jan 2008Signals in the Frequency Domain Interesting signals can be built from a weighted combination of sinusoids Time view: amplitude as a function of time (x(t)) Frequency view: how much of each cosine is in the signal (X(f), called the Fourier Transform) Two basic types of signals:  Periodic (sums of harmonically related sinusoids) Aperiodic (built from a continuum of frequencies, so need an integral to build the signal if in the analog world) Many signals have frequency content that varies with time – need a spectrogram to visualizeEE299 Lecture 414 Jan 2008Two Types of SignalsTIMEFREQfundamental frequencyharmonicsfundamental period‘s’ as in ‘sit’fluteEE299 Lecture 414 Jan 2008Frequency Content vs. Time Take a Fourier Transform over a Window (chunk) of the signal Slide the window over, allowing some overlap Display magnitude of Fourier transform via color Matlab command: spectrogram(x,window,overlap,Nfft,Fs,’yaxis’)slidingwindowoverlap in # of samplesput time on x-axis, frequency on y-axisEE299 Lecture 414 Jan 2008Demo: Seeing SoundEE299 Lecture 414 Jan 2008Which sound goes with which picture?violinbluenoseWhich signal has a time slice that could have this frequency content?This is a sound with energy only at low frequencies, and it does not have clear harmonics as in the violin picture, so it must be speech. In fact it is from the time period of roughly 1.4, the “n” in “blue nose.”The horizontal lines correspond to the harmonics of musical notes.Energy at 0-2kHz is characteristic of speech, as is bursts of high frequency energy.EE299 Lecture 414 Jan 2008Analog vs. Digitalanalog signalx(t)digital signalx(n)tncontinuous in timediscrete in timeSAMPLINGcontinuous in amplitudediscrete in amplitudeQUANTIZATIONSound wave, heart beat, temperature fluctuation, image on film, …Audio file on a CD, signal on a digital computer, Dow Jones daily average, image from a digital cameraEE299 Lecture 414 Jan 2008Sampling: A revolutionary concept!Shannon’s big result:If you sample at least twice as fast as the highest frequency in the signal, you can perfectly recover the original signal.SampleA/DInterpolateD/AFcFs > 2Fctime signalfrequency contentx(t)X(f)easy to work with on a computerSometimes you throw out frequency content to have a smaller FcEE299 Lecture 414 Jan 2008Things that we sample: Speech (8k frequency range)this wav: Fs=16kHz3 seconds = 48k samplesover the phone: Fs=8kHz3 seconds = 24k samples Music (22k frequency range)on a CD: Fs=44.1kHz3 seconds = 132.3k samplesSometimes you throw out frequency content to have smaller FsEE299 Lecture 414 Jan 2008Sampling a Sinusoidcos(2π100t)Fs=1000Fs=500Fs=250Fs=125 < 2*100cos(2π25t)ALIASING!Frequency wraparound, sounds like Fs=25Side note: straight line interpolation does not get back the original, but there’s a smooth function that will work (sinc).cosine frequency in HzEE299 Lecture 414 Jan 2008Aliasing for Video Signals (Wagon Wheel Effect)Sample 8 times per rotation: Perceive correct rotationSample 1 time per rotation: Perceive no rotationSample once every 1.2 rotations: Perceive backwards rotationEE299 Lecture 414 Jan 2008Hearing and Seeing Aliasing Sound demo: higher frequencies sound lower, mixing with actual low frequencies can make it sound muffled See: sound_sampling.m Video demo: videos are sampled in time also (even when using film for the image), so they can also have aliasing, e.g. in old movies the wagon wheel sometimes looks like it is going backwards See: wagon.exe Image content can also be characterized in terms of 2-D cosines, and we’ll see later that we can get aliasing for images