CDS 504: Signals, Systems, Digital Signals, and Middle Ear Acoustics

Flashcards testing core concepts of acoustics, signal parameters, decibel calculations, digital signal processing, filter theory, and outer/middle ear mechanics based on CDS 504 lecture notes.

What is a signal, and what are the specific definitions for mechanical, acoustic, and electrical signals?

A signal is a variation in a parameter over time that carries information. A mechanical signal is a change in position over time; an acoustic signal is a change in pressure over time; and an electrical signal is a change in voltage over time.

What properties are required for a source to vibrate and for sound to travel?

A source requires mass and elasticity to vibrate. Sound requires a medium capable of being set into vibration to travel.

Why cannot traditional sound travel through outer space?

There is no medium available in outer space to transmit the sound wave.

What is a sine wave and what are its three main parameters?

A sine wave is a simple, periodic signal produced by a source vibrating at one frequency. Its three main parameters are frequency, amplitude, and phase.

What are the equations relating frequency ($f$) in Hertz ($\text{Hz}$) and period ($T$) in seconds?

$f = \frac{1}{T}$ and $T = \frac{1}{f}$. If period is given in milliseconds ($T_{\text{ms}}$), frequency is calculated as $f = \frac{1000}{T_{\text{ms}}}$.

What is the frequency of a waveform that has a period of $2\,\text{ms}$?

$500\,\text{Hz}$, calculated using $f = \frac{1000}{2\,\text{ms}} = 500\,\text{Hz}$.

What is the difference between peak amplitude and peak-to-peak amplitude?

Peak amplitude is the maximum displacement from equilibrium. Peak-to-peak amplitude is the total distance from the maximum positive amplitude to the maximum negative amplitude.

If the peak amplitude of a sinusoidal wave is $1\,\text{V}$, what is its peak-to-peak amplitude?

$2\,\text{V}$.

What does RMS stand for, what is its equation for a sinusoid, and what is the RMS of a sinusoid with a $10\,\text{V}$ peak amplitude?

RMS stands for Root Mean Square. For a sinusoid, $\text{RMS} = 0.707 \times \text{Peak}$. If peak amplitude is $10\,\text{V}$, $\text{RMS} = 0.707 \times 10\,\text{V} = 7.07\,\text{V}$.

In a $360^\circ$ cycle of a sine wave, at what phase angles is the wave at equilibrium versus maximum displacement?

The wave is at equilibrium at $0^\circ$, $180^\circ$, and $360^\circ$. It is at maximum displacement at $90^\circ$ (positive) and $270^\circ$ (negative).

What is the speed of sound in air, and what formula describes the effect of temperature on speed?

Sound travels at approximately $344\,\text{m/s}$ in air. The formula for speed based on Celsius temperature ($T_c$) is $v = 331 + 0.61 T_c$.

What equation relates speed ($v$), frequency ($f$), and wavelength ($\lambda$), and what happens to wavelength as frequency increases?

The equation is $v = f \lambda$. If frequency increases while speed stays constant, wavelength decreases.

What is the Inverse Square Law, and what sound level change occurs when distance from a source doubles in a free field?

The inverse square law states that intensity is inversely proportional to the square of the distance from the source. Doubling distance results in an intensity decrease by a factor of 4, or approximately a $6\,\text{dB}$ decrease.

Define sound diffraction, reflection, and refraction.

Diffraction is the bending of sound around objects; reflection is sound bouncing off a surface; refraction is the bending or change in direction of sound due to changes in propagation conditions.

What is damping and what is its equation?

Damping is the reduction or decay of vibration due to friction opposing motion. Its equation is $df = \ln\left(\frac{A_1}{A_2}\right)$.

What is Weber's Law?

Weber's Law states that the minimum detectable change in a stimulus is proportional to the size of the original stimulus.

What is the reference pressure for $\text{dB SPL}$ and what is the formula to calculate it?

The reference pressure ($p_0$) is $20\,\mu\text{Pa}$. The equation is $\text{dB SPL} = 20 \log_{10}\left(\frac{p}{p_0}\right)$.

What is the difference between $\text{dB HL}$ and $\text{dB SL}$?

$\text{dB HL}$ (Hearing Level) is the reference scale used in clinical hearing testing. $\text{dB SL}$ (Sensation Level) is the amount a stimulus level is above an individual's specific hearing threshold.

If a patient's threshold is $30\,\text{dB HL}$ and a tone is presented at $50\,\text{dB HL}$, what is the level in $\text{dB SL}$?

$20\,\text{dB SL}$ (calculated as $50\,\text{dB HL} - 30\,\text{dB HL} = 20\,\text{dB SL}$).

What are $\text{dB(A)}$, $\text{dB(C)}$, and $\text{dB(Z)}$ weightings?

$\text{dB(A)}$ follows aspects of human auditory perception and is used for environmental noise measurements; $\text{dB(C)}$ has a flatter frequency response; $\text{dB(Z)}$ represents zero weighting.

What is the resulting level when combining two equal-intensity sound sources, and what is the general formula for $N$ equal sources?

Combining two equal sound sources increases the sound level by approximately $3\,\text{dB}$ (e.g., $50\,\text{dB} + 50\,\text{dB} = 53\,\text{dB}$). The formula for $N$ equal sources is $\text{dB}_N = \text{dB}_i + 10 \log_{10}(N)$.

What are the three steps required to combine unequal decibel sound levels?

1. Convert each dB value to linear intensity. 2. Add the linear intensities together. 3. Convert the combined linear intensity back to dB.

What is the Principle of Superposition?

The principle that the net response from multiple stimuli is the sum of the responses that each stimulus would produce individually, accomplished by adding wave amplitudes at each point in time.

What is Fourier's Theorem?

Fourier's Theorem states that any arbitrary waveform can be represented as a sum of individual sine tones.

What harmonic components are contained in a sawtooth wave versus a square wave?

A sawtooth wave contains all harmonics (even and odd). A square wave contains odd harmonics only.

What are acoustic beats and when are they typically heard?

Beats are periodic intensity variations resulting from combining two tones with different but close frequencies. They are typically heard when the frequency difference is less than approximately $20\text{--}30\,\text{Hz}$.

What is the difference between a condensation click and a rarefaction click?

A condensation click has positive amplitude and a $+90^\circ$ phase. A rarefaction click has negative amplitude and a $-90^\circ$ phase.

What is the difference between envelope and temporal fine structure (TFS)?

The envelope is the slowly changing overall amplitude of a sound wave, whereas temporal fine structure (TFS) consists of the fast phase changes within the sound.

How does Speech-Shaped Noise (SSN) differ spectrally from white noise?

White noise has equal energy in every $1\text{-Hz}$-wide band across all frequencies. Speech-shaped noise (SSN) has greater low-frequency amplitudes than high-frequency amplitudes.

What factors determine how much acoustic masking occurs?

The frequency overlap between the masker and target sound is critical; greater frequency overlap produces greater masking.

What formula calculates the number of discrete levels in quantization based on bit depth $n$?

$\text{Levels} = 2^n$. For example, 8-bit quantization yields $256$ levels ($2^8$) and 16-bit yields $65{,}536$ levels ($2^{16}$).

What is aliasing and what threshold prevents it?

Aliasing occurs when a signal is sampled too slowly, causing the digitized signal to inaccurately represent the original signal. It is avoided by sampling above the Nyquist frequency, which is half of the sampling rate ($\text{Nyquist} = \frac{f_s}{2}$).

If a system sampling rate ($f_s$) is $20{,}000\,\text{Hz}$, what is its Nyquist frequency?

$10{,}000\,\text{Hz}$ (calculated as $\frac{20{,}000}{2}$).

What is a transfer function and its basic equation?

A transfer function describes how a system alters an input signal to produce an output signal. Its equation is $\text{Output} \div \text{Input}$.

What is filter quality factor ($Q$) and its formula?

$Q$ describes filter sharpness and is calculated as $Q = \frac{\text{CF}}{\text{BW}}$, where $\text{CF}$ is center frequency and $\text{BW}$ is bandwidth. Narrower bandwidth yields a higher $Q$.

How do narrow and wide filter banks trade off resolution?

A narrow filter bank provides better spectral/frequency detail but poorer temporal resolution. A wide filter bank provides better temporal resolution but poorer spectral detail.

What frequency region does the pinna resonance boost, and what function does it serve?

The pinna boosts frequencies between approximately $2000\text{--}7000\,\text{Hz}$ and alters the spectrum to assist with sound localization.

What are the three middle-ear ossicles in anatomical order, and which structures do the first and last contact?

The order is Malleus $\rightarrow$ Incus $\rightarrow$ Stapes. The malleus contacts the tympanic membrane and the stapes contacts the oval window.

What are the three main mechanisms of middle-ear impedance matching?

1. Area difference between the tympanic membrane and oval window. 2. Lever action of the ossicles. 3. Buckling of the tympanic membrane.

What type of hearing loss is caused by middle-ear pathologies, and how much hearing loss can occur if ossicles are absent?

Middle-ear pathologies typically cause conductive hearing loss. Absence of the ossicles can cause approximately $60\,\text{dB}$ of hearing loss.