Crash Course in Digital Signal Processing Signals and Systems Conversion Digital Signals and Their Spectra Digital Filtering Speech, Music, Images and More DSP-G 1.1 Signals and Systems Signals Something that carry information from one place to another Represented mathematically as functions of one or more independent variables, e.g., x(t) Analog signals take any value from a continuum of values; are defined at every instant of time Digital signals defined at only a finite number of levels and points in time DSP-G 1.2
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256 Hz 512 Hz DSP-G 1.7 DSP-G 1.8
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AVI DSP-G 1.11 Systems Something that can analyze, combine, modify, record, or play back signals; e.g., image compression system, speech recognition system, digital filters, etc. Mathematically, a transformation or an operator that maps an input signal into an output signal The operations are usually referred to as signal processing DSP-G 1.12
Conversion Analog-to-Digital (A/D) Conversion Two steps sampling and quantization Sampling Occur at regular intervals called sampling periods Sample and hold at each sampling point, the value of the analog signal is held steady until the next sampling point DSP-G 1.13 Conversion (cont.) Analog-to-Digital (A/D) Conversion Sampling (cont.) Aliasing if sampling is too slow, important signal characteristics can be lost Acquisition time the amount of time required for the act of sampling DSP-G 1.14
Conversion (cont.) Analog-to-Digital (A/D) Conversion (cont.) Quantization Quantize and digitize the analog values Quantization select the quantization level that approximates the sample-and-hold value as closely as possible Digitization assign a binary digital code that identifies the quantization level Quantization error the difference between the analog and digital value The average of the square of the quantization errors is σ 2 = Q e 12 DSP-G 1.15 Conversion (cont.) DSP-G 1.16
Conversion (cont.) Digital-to-Analog (D/A) Conversion Step 1 convert each digital code into an analog level Zero-order-hold the analog level is held steady for the duration of a sampling period Step 2 smooth the zero-order-hold signal DSP-G 1.17 Conversion (cont.) A/D and D/A conversion DSP-G 1.18
Digital Signal and Their Spectra Time domain representation of the digital signal the signal variations are displayed against time Spectrum a representation of the frequency element that are present in a signal Frequency domain representation of the digital signal Low frequency signals are constant or change slowly over time; while high frequency signals change quickly with time DSP-G 1.19 Digital Signal and Their Spectra (cont.) DSP-G 1.20
Digital Signal and Their Spectra (cont.) An example piano note Each piano note consists of many harmonic frequencies, all multiples of a fundamental frequency a single piano note (middle C) DSP-G 1.21 Digital Signal and Their Spectra (cont.) An example piano note (cont.) a piano chord (CEG) DSP-G 1.22
Digital Filtering Digital filter change the nature of a signal Change the frequency characteristics of a signal let some frequencies in the signal pass while block others Low pass filter let low frequencies through while block high frequencies High pass filter let high frequencies through while block low frequencies Band pass filter allow a band of frequencies to pass Band stop filter allow all frequencies outside a band to pass Cut-off frequency the corner frequency of the filter DSP-G 1.23 Digital Filtering (cont.) 男低音男高音次高音女高音 DSP-G 1.24
Digital Filtering (cont.) An example the piano chord DSP-G 1.25 Applications of DSP Applications of DSP Speech speech recognition, speech synthesis Music recordings, mixer, animal sounds Image image synthesis, image enhancement, morphing, 3-D display, visual inspection, robot vision Communication cellular phone, modem, audio and video transmission, etc. DSP-G 1.26