Sound and Its Representations Lecture 6 PDF

Sound and Its Representations Lecture 6 2024  Objective of this Lecture Explain the process of sound digitization Distinguish between time domain and frequency domain representations of sound Interpret amplitude and phase spectra...

Sound and Its Representations Lecture 6 2024  Objective of this Lecture Explain the process of sound digitization Distinguish between time domain and frequency domain representations of sound Interpret amplitude and phase spectra Understand the concept of complex periodic signals and harmonics 2024 Department of Rehabilitation Health Sciences  Sound Digitization What a microphone does A microphone converts, or transduces, fast variation in acoustic pressure to fast changing voltage over time voltage 2024 Department of Rehabilitation Health Sciences  Sound Digitization From analogue to digital 2024 Department of Rehabilitation Health Sciences  Sound Digitization From analogue to digital Sample the voltage that represent sound pressure at discreet intervals A digital audio recording is characterised by : 1. Sampling rate or frequency sample rate (Fs) Which is how many times per second do we measure the sound pressure 2. Bit depth (also known as sample size) How precisely do we measure the sound pressure 2024 Department of Rehabilitation Health Sciences  Sound Digitization Sample the sound pressure at discreet intervals A digital audio recording is a series of sample values e,g,: {4,4,2,-1,-3,-4,-4,-3,0,3} by : Combined with information needed to interpret the sample values ( e.g. sample rate, Fs) 2024 Department of Rehabilitation Health Sciences  Sound Digitization Sampling: The process of converting continuous sound to a series of discrete numbers. Sample: A single numerical measurement of the sound wave's amplitude at a specific point in time Sample rate is the number of audio samples taken per second. It determines how accurately digital recording captures a soundwave. Thousands of samples per second are needed for accurate reproduction. Higher sampling rates capture more details of the original sound. Sample rates are measured in kilohertz (kHz). 44.1 kHz is a common sampling rate, meaning 44,100 samples per second. 2024 Department of Rehabilitation Health Sciences  Sound Digitization The Process of Digital Sound Storage 1. Sound waves are converted to electrical current using a microphone. 2. A digitizer (like those in computer sound cards) acts as a fast digital voltmeter. 3. The digitizer makes thousands of measurements per second, converting the continuous voltage into a series of numbers (samples) P 2024 Department of Rehabilitation Health Sciences  Sound Digitization How fast to sample The Nyquist-Shannon sampling theorem Key Idea: To capture a sound accurately, sample it at least twice as fast as its highest frequency. Formula: Sampling Rate ≥ 2 × Highest Frequency Human Hearing: We hear up to ~20,000 Hz, so we need at least 40,000 samples/second. CD Quality: Uses 44,100 samples/second to cover full hearing range. 2024 Department of Rehabilitation Health Sciences  Sound Digitization understanding sample rates is important for several reasons: Modern hearing aids use digital signal processing. Understanding sample rates can help you better adjust and program these devices for optimal patient outcomes. Many speech analysis tools use digital audio. So, knowing about sample rate can help you choose and use software. Essential for research application 2024 Department of Rehabilitation Health Sciences  Representation of Sounds- Time vs Frequency Domain The graphs that we have used up to this point for representing either vibratory motion or the air pressure disturbance created by this motion are called time domain representation. Time Domain Representation Shows how instantaneous displacement or air pressure varies over time. Waveform visualization Useful for temporal patterns Time Domain Representation Shows what frequencies are present and their respective amplitudes and phases Also known as a spectrum Types: Amplitude Spectrum and Phase Spectrum 2024 Department of Rehabilitation Health Sciences  Representation of Sounds- Types of Frequency Domain 1. Amplitude Spectrum X-axis: Frequency Y-axis: Amplitude Shows the strength of each frequency component in the sound. 2. Phase Spectrum X-axis: Frequency Y-axis: Phase angle (0° to 360°) Shows the phase relationship between different frequency components Interpreting Phase: 1. 0°: Waveform starts at zero, moving upward 2. 90°: Waveform starts at peak positive amplitude 3. 180°: Waveform starts at zero, moving downward 4. 270°: Waveform starts at peak negative amplitude 2024 Department of Rehabilitation Health Sciences  Representation of Sounds- Types of Frequency Domain Figures to clarify the phase of the waves 2024 Department of Rehabilitation Health Sciences  Representation of Sounds- Types of Frequency Domain time and frequency domain representations of three sinusoids. Period: 10 ms, Freq: 100 Hz, Amp: 400, Phase: 90 Amplitude Spectrum Phase Spectrum 200 400 360 Inst. Air Pressure 100 300 270 Amplitude Phase 0 200 180 -100 100 90 -200 0 0 0 100 200 300 400 500 0 100 200 300 400 500 0 5 10 15 20 25 30 Frequency (Hz) Frequency (Hz) Period: 5 ms, Freq: 200 Hz, Amp: 200, Phase: 180 200 400 360 Inst. Air Pressure 100 300 270 Amplitude Phase 0 200 180 -100 100 90 -200 0 0 0 100 200 300 400 500 0 100 200 300 400 500 0 5 10 15 20 25 30 Frequency (Hz) Frequency (Hz) Period: 2.5 ms, Freq: 400 Hz, Amp: 200, Phase: 270 200 400 360 Inst. Air Pressure 100 300 270 Amplitude Phase 0 200 180 -100 100 90 -200 0 0 0 100 200 300 400 500 0 100 200 300 400 500 0 5 10 15 20 25 30 Frequency (Hz) Frequency (Hz) Time (msec) TIME DOMAIN FREQUENCY DOMAIN 2024 Department of Rehabilitation Health Sciences  Complex Periodic Signals and Harmonics Key Terms Fundamental Period (t₀):Time to complete one cycle of the complex pattern. Fundamental Frequency (f₀): Number of cycles completed in one second (f₀ = 1/t₀). Harmonic: Frequency component that is a whole number multiple of the fundamental frequency. Harmonic Spectrum: Shows energy at the fundamental frequency and its whole number multiples. Example: If f₀ = 100 Hz, harmonics will be at 100 Hz, 200 Hz, 300 Hz, etc. 2024 Department of Rehabilitation Health Sciences  Complex Periodic Signals and Harmonics Fundamental frequency has two equivalent definitions from the figures: Time domain: Cycles of complex pattern per second Frequency domain: Lowest harmonic in spectrum 2024 Department of Rehabilitation Health Sciences  Aperiodic Signals Sounds that do not show a repeating pattern in the time domain Examples in speech: fricatives (/f/, /s/), stop consonants (/b/, /d/, /g/, /p/, /t/, /k/) Non-speech examples: cymbal crash, radio static Types of Aperiodic Sounds: 1. Continuous Aperiodic Sounds (Noise) Longer duration Examples: /s/ and /f/ sounds in speech, white noise 2. Transients Very brief duration Examples: pops, clicks, stop consonant releases 2024 Department of Rehabilitation Health Sciences  Aperiodic Signals White Noise 100 200 All aperiodic sounds -- both Inst. Air Pres. (UPa) 80 100 Amplitude continuous and transient -- are 0 60 40 complex in the sense that they -100 -200 20 always consist of energy at 0 10 20 /s/ 30 40 50 0 0 1 2 3 4 5 6 7 8 9 10 100 more than one frequency. 200 Inst. Air Pres. (UPa) 80 100 Amplitude 60 0 40 The characteristic feature of -100 20 -200 aperiodic sounds in the 0 10 20 30 40 50 0 0 1 2 3 4 5 6 7 8 9 10 /f/ frequency domain is a dense or 200 100 Inst. Air Pres. (UPa) 80 continuous spectrum, 100 Amplitude 60 0 40 -100 20 -200 0 0 10 20 30 40 50 0 1 2 3 4 5 6 7 8 9 10 TIME (msec) Frequency (kHz) TIME DOMAIN FREQUENCY DOMAIN 2024 Department of Rehabilitation Health Sciences  Aperiodic Signals- Noises The intensity of each frequency 1. White Noise I n t component is the same Definition: Equal intensity at all frequencies e d n B s Characteristics: Flat amplitude spectrum i S t P y L I n 2. Narrow Band Noise Frequency in Hertz (Hz) Definition: Filtered white noise around a specific center frequency Noise – Narrow Band Characteristics: Limited frequency range Often centered around audiometric test I n t e d n B frequencies dB s i S t P y L I n.25k.5k 1k 2k 4k 8k 16k Frequency in Hertz (Hz) 2024 Department of Rehabilitation Health Sciences  Fourier Analysis Developed by Joseph Fourier in the 19th century Fundamental principle: Any complex waveform can be decomposed into a sum of simple sinusoids The Fourier Transform Converts signals from time domain to frequency domain Reveals the frequency components of a complex signal Outputs: Amplitude spectrum: Shows amplitude of each frequency component Phase spectrum: Shows phase of each frequency component 2024 Department of Rehabilitation Health Sciences  Fourier Analysis FREQUENCY DOMAIN Amplitude TIME DOMAIN 0 200 400 600 800 Frequency (Hz) Inst. Air Pres. Fourier Analyzer Phase Time -> 0 200 400 600 800 Frequency (Hz) 2024 Department of Rehabilitation Health Sciences Thank you