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Preface | |
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Preface to the Original Edition | |
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Introduction | |
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Exercises | |
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Signals in the Real World | |
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The movement of a tuning fork | |
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What is sound? | |
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Converting pressure changes into a more convenient form | |
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Getting back to acoustic signals | |
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Summary | |
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Exercises | |
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Introduction to Signals | |
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Frequency and period of sinusoids | |
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Constructing sinusoids | |
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Using trigonometry to determine the shape of a sinusoid | |
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Phase | |
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Amplitude | |
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Examples of other periodic signals | |
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Aperiodic signals | |
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Peak-to-peak and root-mean-square amplitude measurements | |
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Measuring amplitude;-the relationship between amplitude and intensity | |
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Defining scales | |
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Definition of the intensity scale-dB values | |
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Scale reference points | |
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Taking the logarithm of the ratio | |
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Further features of dB scales | |
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Exercises | |
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Appendix: Exponents and logarithms (to the base 10) | |
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Introduction to Systems | |
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Homogeneity | |
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Additivity | |
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Linearity = homogeneity + additivity | |
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Time invariance | |
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Exercises | |
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A Preview | |
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Exercises | |
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The Frequency Response of Systems | |
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Amplitude responses-the basic concept | |
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Amplitude responses as ratios | |
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Filters | |
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Systems in parallel | |
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Systems in cascade | |
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Band-pass filters | |
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Band-pass responses in simple physical systems | |
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The amplitude response of a cascade of LTI systems | |
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The vocal tract as a linear system | |
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Phase responses | |
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Linear phase responses | |
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Wrapped and unwrapped phase curves | |
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Other phase responses | |
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The phase response of two LTI systems in cascade | |
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The transfer function of LTI systems in cascade | |
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Exercises | |
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Appendix 6.1 | |
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Appendix 6.2 | |
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Appendix 6.3 | |
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The Frequency Characterization of Signals | |
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Adding sinusoids: synthesis | |
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Decomposing periodic waveforms: analysis | |
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The Fourier series of a sawtooth waveform | |
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Amplitude spectrum of a sawtooth wave | |
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Phase spectrum of a sawtooth waveform | |
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The effect of altering the phase of one component | |
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The effect of altering the amplitude of one component | |
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The effect of missing one component out | |
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Spectra of other periodic waveforms | |
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The spectrum of a pulse train | |
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The effect of increasing period with the same duration pulse | |
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Spectra of aperiodic signals | |
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Fourier transform of a transient signal | |
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Random signals | |
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Exercises | |
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Signals Through Systems | |
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Furring a periodic signal through a filter | |
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Speeding things up | |
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Putting a periodic signal through a real low-pass filter | |
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Putting an aperiodic signal through a system | |
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Distortion and the perfect system | |
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Exercises | |
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The Time Characterization of Systems | |
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What can we learn from a system response to a single pulse? | |
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Approximating signals with rectangular pulses | |
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The relationship between the impulse response and the frequency response | |
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Determining the frequency response of a system: a practical example | |
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Exercises | |
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The Relationship Between the Time and Frequency Domains | |
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The spectra of rectangular pulses of varying duration | |
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The spectra of sinusoids of varying duration | |
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'Windowing' signals | |
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'Windowing' non-sinusoidal signals | |
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The relationship between the ordinary and inverse Fourier transform | |
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Time domain and frequency domain relationships for systems | |
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The impulse and amplitude response of simple band-pass filters | |
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Resolution in frequency for different bandwidths | |
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Resolution in time for different bandwidths | |
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Bandwidth versus resolution: a summary | |
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Exercises | |
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The Spectrogram | |
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The basic problem: determining the spectra of real-life signals | |
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Analyzing a sawtooth with a filter bank | |
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Signals that change in time | |
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Whistling through a single band-pass filter | |
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Getting rid of detail: rectification and smoothing | |
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Summary: filtering, rectification and smoothing | |
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Looking across a range of frequencies with a filter bank | |
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Constructing a spectrogram | |
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Displaying spectrograms in a convenient way | |
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Spectrographs | |
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Another approach to making a spectrogram | |
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The graphic equalizer | |
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A spectrum displayed as a bar graph | |
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Converting the height of a bar into the darkness of a trace | |
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Converting the time dimension into the x-axis on a piece of paper | |
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Sections: short-term spectra | |
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The choice of filter bandwidth | |
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Determining a spectrum with filter banks of wide- and narrow-band filters | |
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Resolving two spectral components close in frequency | |
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Wide- and narrow-band spectrograms of an impulse | |
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Resolving two pulses close in time | |
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Wide- and narrow-band spectrograms of quasi-periodic pulse trains | |
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Wide- and narrow-band spectrograms of random signals | |
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Making spectrograms in the time domain | |
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Dividing up a signal into sections | |
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The choice of window length | |
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Analyzing a sinusoid with different window lengths | |
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Long- and short-time spectrograms of two closely spaced sinusoids | |
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Long- and short-time spectrograms of a filtered periodic pulse train | |
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Frequency equalization | |
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Concluding remarks | |
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Exercises | |
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Applications to Hearing | |
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Outer ear | |
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Middle ear | |
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The movement of the basilar membrane | |
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Transduction by the inner hair cells | |
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Making an auditory spectrogram | |
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Exercises | |
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Applications to Speech Production | |
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Source-filter theory of speech production | |
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Amplitude spectrum off /∂/ at a constant voice fundamental frequency | |
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Amplitude spectrum of /∂/ at a different voice fundamental frequency | |
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Spectrographs representation of /∂/ at different voice fundamental frequencies | |
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Spectrographs analysis of vowels with a changing fundamental | |
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Properties of other vowel sounds | |
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Diphthongal vowels | |
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Voiceless fricatives | |
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Summary and comments | |
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Exercises | |
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An Introduction to Digital Signals and Systems | |
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Pros and cons of digital techniques | |
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What is an analogue signal? | |
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What is a digital signal? | |
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Digital systems | |
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Quantization | |
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Sampling | |
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How fast does sampling have to be? The sampling theorem | |
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Sampling complex signals | |
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Processing the digital signal | |
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Reconverting back to analogue form | |
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A digital amplifier | |
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A simple digital low-pass filter | |
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A simple digital high-pass filter | |
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A simple infinite impulse response system | |
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FIR and IIR systems | |
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Concluding remarks | |
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Exercises | |
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Appendix | |
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Index | |