1. AUDIO TECHNOLOGY 2 Signal Representation

2. Audio Audio is a wave resulting from air pressure disturbance that reaches our eardrum generating the sound we hear. –Humans can hear frequencies in the range 20-20,000 Hz. ‘Acoustics’ is the branch of physics that studies sound

3. Characteristics of Audio Audio has normal wave properties –Reflection(انعكاس) –Refraction (انكسار) –Diffraction الحيود A sound wave has several different properties: –Amplitude (loudness/intensity) –Frequency (pitch) –Envelope (waveform)

4. Audio Amplitude Audio amplitude is often expressed in decibels (dB) Sound pressure levels (loudness or volume) are measured in a logarithmic scale (deciBel, dB) used to describe a ratio –Suppose we have two loudspeakers, the first playing a sound with power P 1, and another playing a louder version of the same sound with power P 2, but everything else (how far away, frequency) is kept the same. –The difference in decibels between the two is defined to be 10 log 10 (P 2 /P 1 ) dB

5. Audio Amplitude In microphones, audio is captured as analog signals (continuous amplitude and time) that respond proportionally to the sound pressure, p. The power in a sound wave, all else equal, goes as the square of the pressure. –Expressed in dynes/cm 2. The difference in sound pressure level between two sounds with p 1 and p 2 is therefore 20 log 10 (p 2 /p 1 ) dB The “acoustic amplitude” of sound is measured in reference to p 1 = p ref = 0.0002 dynes/cm 2. –The human ear is insensitive to sound pressure levels below p ref.

6. Audio Amplitude IntensityTypical Examples 0 dBThreshold of hearing 20 dBRustling of paper(حفيف ورق) 25 dBRecording studio (ambient level) 40 dBResident (ambient level) 50 dBOffice (ambient level) 60 - 70 dBTypical conversation 80 dBHeavy road traffic 90 dBHome audio listening level 120 - 130 dBThreshold of pain 140 dBRock singer screaming into microphone

7. Audio Frequency Audio frequency is the number of high-to-low pressure cycles that occurs per second. In music, frequency is referred to as pitch. Different living organisms have different abilities to hear high frequency sounds Dogs: up to 50KHz Cats: up to 60 KHz Bats: up to 120 KHz Dolphins: up to 160KHz Humans: Called the audible band. The exact audible band differs from one to another and deteriorates with age.

8. Audio Frequency The frequency range of sounds can be divided into Infra sound0 Hz– 20 Hz Audible sound 20 Hz– 20 KHz Ultrasound20 KHz – 1 GHz Hypersound1 GHz – 10 GHz Sound waves propagate at a speed of around 344 m/s in humid air at room temperature (20  C) Hence, audio wave lengths typically vary from 17 m (corresponding to 20Hz) to 1.7 cm (corresponding to 20KHz). Sound can be divided into periodic (e.g. whistling wind, bird songs, sound from music) and nonperiodic (e.g. speech, sneezes and rushing water).

9. Audio Frequency Most sounds are combinations of different frequencies and wave shapes. Hence, the spectrum of a typical audio signal contains one or more fundamental frequency, their harmonics, and possibly a few cross- modulation products. Fundamental frequency Harmonics The harmonics and their amplitude determine the tone quality or timbre.

10. Audio Signal Representation Waveform representation –Focuses on the exact representation of the produced audio signal. Parametric form representation –Focuses on the modeling of the signal generation process. –Two major forms Music synthesis (MIDI Standard) Speech synthesis

11. An Audio Signal

12. What is a signal Changes in medium (i.e air pressure, incident photons) are the signals we use to interpret the world. They are time varying fluctuation in some physical medium. They are continuous –i.e. describable by real numbers, not as integers. Since they have real continuous measurements known as analogue signals

13. Sinusoidal Signals Fundamental period (T0): The shortest interval that a signal repeats Fundamental frequency (f0): f0 =1/ T0 T0T0 Note: frequency is measured in Hertz Hz (1/s)

14. t = linspace(0,1,1001); A = 5; f = 4; p = pi/8; x = A*cos(2*pi*f*t + p); plot(t, x) Repeat the above code with different values of (f ) and plot the signal for each value of f and see the difference between the plots

15. Concept of Bandwidth. f min (f max ):lowest (highest) frequency of the signal components. Bandwidth : B.W= f max - f min. A non-bandlimited signal can be converted to band limited by filtering - Bandwidth of a signal is a critical feature when dealing with the transmission of this signal - A communication channel usually operates only at certain frequency range (called channel bandwidth). The signal will be severely attenuated if it contains frequencies outside the range of the channel bandwidth. To carry a signal in a channel, the signal needed to be modulated from base band to the channel bandwidth. Multiple narrowband signals may be multiplexed to use a single wideband channel

16. Signal Filtering A filter is device or process that remove from the signal some unwanted component or feature h(t) x(t) Y(t). Lowpass -> smoothing, noise removal Highpass -> edge/transition detection Bandpass -> Retain only a certain frequency range Low Pass High PassBand Pass

17. Bandwidth of Multimedia Signals/Channels

18. Waveform Representation Audio Capture Sampling & Digitization Storage or Transmission Receiver Digital to Analog Playback (speaker) Audio Source Human Ear Audio Generation and Playback

19. Digitization To get audio (or video for that matter) into a computer, we must digitize it (convert it into a stream of numbers). This is achieved through sampling, quantization, and coding.

20. Analog To Digital Conversion ( A / D ) In the case of audio and video, the raw signal starts as analogue electrical signal. To be converted to a form suitable for computer manipulation, the signal must be digitized. Digital data is based on values either 0 or 1. Sampling and Quantization Three Processes in A/D Conversion

21. Sampling Sampling: The process of converting continuous time into discrete values. Analog signal Discrete signal t

22. 1.Time axis divided into fixed intervals 2.Reading of the instantaneous value of the analog signal is taken at the beginning of each time interval (interval determined by a clock pulse) 3.Frequency of clock is called sampling rate or sampling frequency The sampled value is held constant for the next time interval (sampling and hold circuit) Sampling Process

23. Nyquist theorem (Sampling Theorem) –The necessary condition of reconstructing a continuous signal from the sampling version is that the sampling frequency fs > 2f max f max is the highest frequency component in the signal. If a signal’s frequency components are restricted in [f1, f2], we need fs >2 (f2-f1). 1.Sampling : take samples at time nT  T: sampling period;(n=0,1,2,3,4……..)  fs = 1/T: sampling frequency Note: If the sampling rate is predetermined then we must filter out frequencies above the Nequist limit to avoid aliasing.

24. Example Suppose the maximum frequency in a signal was 10 KHz, what the sampling frequency should be? Also, what is the sampling time? Solution Since, then 2f max = 20KHz. That means f s should be greater than or equal to 20 KHz. That also means that That means that the sampling time T s should be less than or equal to 50  s. For the signal to be reconstructed accurately.

25. Signal Period T, f = 1/T Intuitively T should >= 2Ts

26. What will happen if the sampling rate is too low ? Aliasing: When the sampling theorem condition (Nyquist Condition) is not met. Components of frequencies higher than half The sampling rate appear as frequencies lower than half the sampling rate. which implies that the original analogue signal frequencies can not be reconstructed accurately from its digital (sampled ) counterpart

27. Example: determine the rate of the sampler and the bandlimiting filter in an encoder which is to be used for digitization of analog signal which has a bandwidth from 15 Hz through to 10 KHz assuming the digitized signal: I: is to be stored in the memory of a computer II: is to be transmitted over a channel which has a bandwidth from 200 Hz through to 3.4 KHz Solution: The Nyquist sampling rate must be twice the highest frequency component of the signal or transition channel. Hence I: the sampling must be at least 2x10=20 KHz or 20 Ksps and the bandwidth of the bandlimitting filter must be from 0 to 10 KHz II: The sampling rate must be at least 2X3.4=6.8 KHz or 6.8 Ksps

28. 2. Quantization: Converts continuous– Amplitude signal to discrete- Amplitude signal. These could be equal intervals, and they could be unequal. To make thing easier we will deal with equal quantization intervals  D represents the Dynamic Range of the signal for the signal changes from Vm to –Vm, D=Vmax-Vmin  Quantization Interval ( Step)  Number of quantization levels L  B : Number of bits required to represent a sample ( Sample Resolution ) 3 2 -2 -3 -4 Range: D Each codeword corresponding to a nominal amplitude level which at the center of the corresponding quantization interval. Hence, the actual signal level may differ from this by up ± Δ/2

29. Quantization The process of converting continuous sample values into discrete values. –Size of quantization interval is called quantization step. –How many values can a 4-bit quantization represent? 8-bit? 16-bit? The higher the quantization, the resulting sound quality.............

30.  /2 3  /2 5  /2 7  /2 -  /2 -3  /2 -5  /2 -7  /2 Original signal Sample value Approximation 3 bits / sample  The ratio of the peak amplitude of a signal to minimum amplitude is known as a dynamic range of signal, D, Normally it is quantified using decibels (dB) dB Quantization Error : The difference between the real value and the quantized representation

31. Example : storing each sample with only two bits (4 possible stored states:( 0, 1, 2, 3). Vmax=4, Vmin=0 Ts=0.1 sec

33. For each signal value s[n], we then round the true value to the nearest of the four levels. This process of signal rounding is a form of quantization.

34. B= 3 bits B= 4 bits

35. N= 16 bits Shown an analogue signal quantized using 3 bits, 4 bits, and 16 bits. Notice how accurate the samples are when stored using 16 bits.

36. Notes on Quantization The lower the levels, the higher the error, which leads to quality degradation. The more the levels, the more the bits and the more bandwidth used: Higher cost. Conclusion: One should make a tradeoff between (1) and (2) N Δ ResolutionL There is an inverse relation between: L, B, and the resolution on one hand and Δ and e q on the other hand. B

37. The Effect of Quantization In the following pictures, Lenna has been quantized into a number of different levels. 8 levels 128 levels256 levels

38. Example: An analog signal has a dynamic range of 40 dB, Determine the magnitude of the quantization noise relative to minimum signal amplitude if the quantizer uses 1) 6 bits and 2) 10 bits and 1) B= 6 bits 2) B= 10 bits with 6 bits the quantization noise is greater than and hence is unacceptable while with 10 bits the quantization noise is less than hence will have much reduced effect.

39. Bit Rate of Digital Signal Sampling rate: sample / sec Quantization Resolution : B Bit/ Sample Ex1: speech signal sampled at 8 KHz, quantized to 8 bit/sample, Bit-Rate=8*8 = 64 Kbps Ex2: music signal sampled at 44 KHz, quantized to 16 bit/sample, Bit- Rate=44*16=704 Kbps

40. Monophonic digitized audio signal Stereo digitized audio signal Ex: A 10 second monophonic audio signal recording at 22.05 kHz, 8-bit resolution would be 22.05*10*(8/8)*1=220.500 bytes Ex : A 10 second stereo recording at 44.1 kHz, 16-bit resolution (meaning CD-quality) would be 10*44.1*(16/8)*2=1.764 Mb How to determine the size in (byte) of digitized audio signal ?