MIT6_003S10_lec18_handout

MIT6_003S10_lec18_handout - 6.003: Signals and Systems...

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6.003: Signals and Systems Lecture 18 April 13, 2010 6.003: Signals and Systems Discrete-Time Frequency Representations Signals and/or Systems Two perspectives: feedback and control (focus on systems) + controller plant sensor X Y Is the system stable? signal processing (focus on signals) target image Learn about target ( signal ) from the image ( signal ). Fourier methods are especially useful in signal processing. April 13, 2010 Historical Perspective Signal Processing: Acoustical Broad range of CT signal-processing problems: audio radio (noise/static reduction, automatic gain control, etc.) telephone (equalizers, echo-suppression, etc.) hi-fi (bass, treble, loudness, etc.) television (brightness, tint, etc.) radar and sonar (sensitivity, noise suppression, object detection) ... Increasing important applications of DT signal processing: MP3 JPEG MPEG MRI Mechano-acoustic components to optimize frequency response of loudspeakers: e.g., “bass-reflex” system. driver reflex port Signal Processing: Acoustico-Mechanical Passive radiator for improved low-frequency preformance. driver passive radiator Signal Processing: Electronic The development of low-cost electronics enhanced our ability to alter the natural frequency responses of systems. 10 1 10 2 10 3 10 4 10 5 70 80 90 100 110 Frequency (Hz) Magnitude (dB) Eight drivers faced the wall; one pointed faced the listener. Electronic “equalizer” compensates for limited frequency response. 1
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± ± 6.003: Signals and Systems Lecture 18 April 13, 2010 Signal Processing Modern audio systems process sounds digitally. A/D DT filter D/A x ( t ) y ( t ) x [ n ] y [ n ] Signal Processing Modern audio systems process sounds digitally. Texas Instruments TAS3004 2 channels 24 bit ADC, 24 bit DAC 48 kHz sampling rate 100 MIPS $7.70 ($4.81 in bulk) Control PWR_DN TEST AINRP AINRM AINLM AINLP 24-Bit Stereo ADC RINA RINB AINRM AINRP AINLM AINLP LINA LINB CS1 SDA SCL Controler GPI0 GPI1 GPI2 GPI3 GPI4 GPI5 24-Bit Stereo DAC CAP_PLL MCLK XTALO MCLKO CLKSEL SDIN2 SDIN1 SDATA Control LRCLK/O SCLK/O SDOUT1 L L+R SDOUT2 32-Bit Audio Signal Processor AOUTL VCOM AOUTR L+R R 32-Bit Audio Signal Processor OSC/CLK Select PLL Reference Voltage Supplies Analog Supplies Digital IFM/S RESET INPA ALLPASS XTALI/ Figure 1- 1. TAS3004 Block Diagram AV SS(REF) V RFILT DD SS REFM DV REFP I 2 C Control Analog Format Output SDOUT0 Logic Control Register Courtesy of Texas Instruments. Used with permission. DT Fourier Series and Frequency Response Complex Geometric Sequences Today: frequency representations for DT signals and systems. Complex geometric sequences are eigenfunctions of DT LTI systems.
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MIT6_003S10_lec18_handout - 6.003: Signals and Systems...

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