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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 | |