Digital Techniques For Processing 2-Dimensional Analog Signals
An Analog or Analogue signal is any continuous signal for which the time varying feature (variable) of the signal is a representation of some other time varying quantity, i.e Analogous to another time varying signal. It differs from a digital signal in terms of small fluctuations in the signal which are meaningful. Analog is usually thought of in an electrical context; however, mechanical, pneumatic, hydraulic, & other systems may also convey Analog signals.An Analog signal uses some property of the medium to convey the signal's information. For example, an aneroid barometer uses rotary position as the signal to convey pressure information. Electrically, the property most commonly used is voltage followed closely by frequency, current, & charge.
The biggest advantage is the fine definition of the Analog Signal which has the potential for an infinite amount of signal resolution. Compared to digital signals, Analog signals are of higher density.
Another advantage with Analog signals is that their processing may be achieved more simply than with the digital equivalent. An Analog signal may be processed directly by Analog components, though some processes aren't available except in digital form.
The primary disadvantage of Analog signaling is that any system has noise - i.e., random unwanted variation. As the signal is copied & re-copied, or transmitted over long distances, these apparently random variations become dominant. Electrically, these losses can be diminished by shielding, good connections, & several cable types such as coaxial or twisted pair.
The effects of noise create signal loss & distortion. This is impossible to recover, since amplifying the signal to recover attenuated parts of the signal amplifies the noise (distortion/interference) as well. Even if the resolution of an Analog signal is higher than a comparable digital signal, the difference can be overshadowed by the noise in the signal.
Telephone voice signal is Analog. The intensity of the voice causes electric current variations. At the receiving end, the signal is reproduced in the same proportion. Hence the electric current is a ‘MODEL' but not one's voice since it is an electrical representation or Analog of one's voice.
The term digital signal is used to refer to more than one concept. It can refer to discrete-time signals that have a discrete number of levels, for example a sampled & quantified Analog signal, or to the continuous-time waveform signals in a digital system, representing a bit-stream. In the first case, a signal that is generated by means of a digital modulation method which is considered as converted to an Analog signal, while it is considered as a digital signal in the second case.
An Analog signal is a datum that changes over time—say, the temperature at a given location; the depth of a certain point in a pond; or the amplitude of the voltage at some node in a circuit—that can be represented as a mathematical function, with time as the free variable (abscissa) & the signal itself as the dependent variable (ordinate). A discrete-time signal is a sampled version of an Analog signal: the value of the datum is noted at fixed intervals (for example, every microsecond) rather than continuously.
What Is Dsp?
DSP, or Digital Signal Processing, as the term suggests, is the processing of signals by digital means. A signal in this context can mean a number of different things. Historically the origins of signal processing are in electrical engineering, & a signal here means an electrical signal carried by a wire or telephone line, or perhaps by a radio wave. More generally, however, a signal is a stream of information representing anything from stock prices to data from a remote-sensing satellite. The term "digital" comes from "digit", meaning a number (you count with your fingers - your digits), so "digital" literally means numerical; the French word for digital is numerique. A digital signal consists of a stream of numbers, usually (but not necessarily) in binary form. The processing of a digital signal is done by performing numerical calculations.
Signals commonly need to be processed in a variety of ways. For example, the output signal from a transducer may well be contaminated with unwanted electrical "noise". The electrodes attached to a patient's chest when an ECG is taken measure tiny electrical voltage changes due to the activity of the heart & other muscles. The signal is often strongly affected by "mains pickup" due to electrical interference from the mains supply. Processing the signal using a filter circuit can remove or at least reduce the unwanted part of the signal. Increasingly nowadays, the filtering of signals to improve signal quality or to extract important information is done by DSP techniques rather than by Analog electronics.
Development Of Dsp
The development of digital signal processing dates from the 1960's with the use of mainframe digital computers for number-crunching applications such as the Fast Fourier Transform (FFT), which allows the frequency spectrum of a signal to be computed rapidly. These techniques were not widely used at that time, because suitable computing equipment was generally available only in universities & other scientific research institutions.
The application of 2D analog signal is very vast. Its usage can be seen in our various day to day life processes. As few of them has been discussed here which includes Image Processing and Medical Application in Scanning purposes.
A. Image Processing
Synthetic Aperture Radar (SAR) image of Washington D.C. produced by 2D DSP.
SAR images look the same, regardless of the time of day or night, or weather conditions.
(The radar image looks basically the same at 11 am or 11 pm, on a clear day or a foggy day)
Two-Dimensional (2D) digital signal processing (2D DSP) is used to produce Synthetic Aperture Radar (SAR) images from microwave radar echoes. The first several stages of the processing primarily involve digital filters & sampling rate changes. The last stage of the processing is implemented by a two-dimensional (2D) FFT. The output of the 2D FFT is a 2D matrix of complex numbers. Each complex number corresponds to a picture element (pixel) in the output image. The magnitude of each 2D FFT output complex number is converted to a gray level (brightness, as an indication of microwave reflectivity) for each pixel. There are usually 256 possible gray levels, corresponding to one byte, for each pixel. The pixels are usually compressed with an algorithm such as JPEG for efficient storage.
The above image in Figure 1 was compressed in the JPEG format to reduce the size of this document. JPEG is based on the discrete cosine transform (DCT), which is similar to the discrete Fourier transform (DFT). JPEG is now used for images on Internet web pages. When you go to a web page that includes an image, your web browser downloads the JPEG coeffcients & then computes the inverse discrete cosine transform (IDCT) to reconstruct the image. The FFT is used to efficiently compute the IDCT.
B. 2D Digital Signal Processing: Medical Imaging Examples
Medical images are produced using the same DSP algorithms as in Synthetic Aperture Radar (SAR) systems. In particular, the last step in the signal processing is a 2D FFT.
G. Hounsfield, a radar engineer, received the Nobel Prize in Medicine for applying SAR signal processing algorithms to medical data. He did “technology transfer” from radar to medicine. The previous medical imaging technology used x-ray film to produce blurry images of bones. Hounsfield applied radar digital signal processing algorithms to medical data to produce detailed images of 2D slices through bones & soft tissue. Some examples of medical images produced by digital signal processing are shown below.
The soft tissue comprising the spinal cord is visible inside the bony spine.
3(a) X-ray Computerized Tomogram (x-ray CT) of a horizontal slice through a spine. Tomogram means “slice.” It is produced by a 2D FFT of digitally filtered x-ray data.
3(b) 3D view of a spine constructed from multiple 2D x-ray CT slices taken at different elevations.
1D Approach To 2D-Signal Processing
After a short review of 1D linear systems the usual method for 2D signal processing will be reviewed. Its merits & disadvantages will be treated briefly. Starting with the problem of processing a sequence of images, a new approach will be proposed, based on the concept of a multiport 1D system, to be described by state equations. In this case some specializations are appropriate, leading to certain properties of the matrices describing these systems. Some stability considerations will be presented as well. The processing of a single image will be treated as a special case.