0.8 Lecture 9:sampling of ct signals

Lecture #9:

SAMPLING OF CT SIGNALS

Motivation:

• Some data acquisition inherently samples a CT signal, e.g., in image acquisition. Signal processing of a CT signal on a digital computer requires that the CT signal be sampled.

• One method of signal processing, recording, or transmission is to convert CT signals to digital signals, process, record, or transmit the digital signals, and then convert the processed digital signals to CT signals.

• Problems with aliasing of sampled signals — distortion.

• Opportunities with aliasing of sampled signals — stop action imaging

Outline:

• Examples of the use of sampling — digital image acquisition, digital audio
• Model of sampling — impulse modulation
• The CTFT of a sampled signal
• Recovering a bandlimited signal from its samples; the Sampling Theorem
• Effects of sampling above, at, or below the Nyquist rate

• Sampling sinusoidal time functions — under and over sampling
• Demonstration of effect of aliasing on audio signals
• Demonstration of stroboscopic illumination
• Sampling images
• Conclusion

I. EXAMPLES OF THE USE OF SAMPLING

Image acquisition — photographic emulsion

Photographic emulsions are generally made with photoreactive crystals of AgBr with grain size in the range 0.04-1.5 μm.

Image acquisition — CCD camera

CCD (charge coupled device) chips are the basis of digital cameras and displays. CCD chips are fabricated with VLSI technology. The phototransducer is a solid-state, back-biased diode whose current is sensitive to light intensity.

Photomicrograph of a CCD camera surface showing portions of 16 unit cells each with dimensions 13 × 11 μm. Each unit cell corresponds to a pixel. The chip has 500 × 582 pixels in an area of 10 × 9.3 mm.

Image acquisition — retina

The human retina contains photoreceptors (rods and cones) whose dimensions and spacings are of the order of 10 μm.

Image acquisition — conclusion

Therefore, for each of these image acquisition systems — photographic emulsion, CCD camera, and retina — the light striking the surface of the phototransducer is sampled at discrete points in space (pixels) to produce a discrete time image.

Digital audio — recording system

In a number of applications, analog audio signals (e.g., speech or music) are converted into digital signals and processed by DT systems and then converted back to analog audio. Applications include compact discs, digital audio tape, digital broadcasting, digital telephony, etc. A single channel of such a recording system is shown below. If stereo is recorded then there are two channels — one for the left and the other for the right channel — that are passed through a multiplexer which is typically interposed before the error correction block.