Signal Processing

Signal Processing

A real time signal processing applications compute in each sampling period one or more outputs. Each output x(k) is a weighted sum of n inputs y(i). That is,

The weight a(k, i) are generally known and fixed. This computation transforms the given representation of an object such as voice or radar signal in terms of the input y(i), into another representation in terms of the outputs x(k)’s.

(Low level controller workload is purely or mostly periodic)

Radar System

A signal processing application is typically a part of a larger system. As an example, Figure below shows a block diagram of a passive radar signal processing and tracking system. The system consists of an I/O subsystem that samples and digitizes the echo signal from the radar and then, places the sampled values in a shared memory. An array of digital signal processors processes these sampled values. The data thus produced are analyzed by one or more data processors that not only interface with the display system, but also generate commands to control the radar and select parameters to be used by signal processors in the next cycle of data collection and analysis.

Radar Signal Processing

To search for objects of interest in its coverage area, the radar scans the area by pointing its antenna in one direction at a time. During the time the antenna dwells in a direction, it first sends a short radio frequency pulse. It then collects and examines the echo signal returning to the antenna.

The echo signal consists solely of background noise if the transmitted pulse does not hit any object. On the other hand, if there is a reflective object (e.g., an airplane or storm cloud) at a distance x meters from the antenna, the echo signal reflected by the object returns to the antenna at approximately 2x/c seconds after the transmitted pulse, where c =3×108 meters per second is the speed of light. The echo signal collected at this time should be stronger than when there is no reflected signal. If the object is moving, the frequency of the reflected signal is no longer equal to that of the transmitted pulse. The amount of frequency shift (called Doppler shift) is proportional to the velocity of the object. Therefore, by examining the strength and frequency spectrum of the echo signal, the system can determine whether there are objects in the direction pointed at by the antenna and if there are objects, what their positions and velocities are. (Liu 15)

Gating and Association

Gating and association is used to remove false trace and trajectory. Strong noise and man-made interferences can make signal processing and detection process wrong about the presence of objects a process wrong about the presence of objects. A track record on a non- existing object is called a false return. An application that examines all the track records in order to sort out the false returns from real ones and update the trajectories of detected objects is called a tracker. The tracker assigns each measured value to a trajectory. If the trajectory is of existing one, the measured value assigned to it gives the current position and velocity of the object moving along the trajectory but if the trajectory is new one, the measured value gives the position and velocity of possible new objects. The tracking of the object is performed in two steps: Gating and Association.

Gating

Gating is the process of putting each measured value into one of two categories depending on whether it can or cannot be tentatively assigned to one or more established trajectories. The value is assigned to an established trajectory if it is within a threshold distance ‘G’ from the predicted current position and velocity of the object moving along the trajectory. The threshold ‘G’ is called track gate.

Association

The tracking process completes if after gating every measured value is assigned to at most one trajectory and every trajectory is assigned to at most one measured value. This can occur when radar signal is strong and interferences is low and the density of object is low. Sometimes, the result of gating can be confusing and some measured values are assigned to more than one trajectory is assigned to more than one measured value. In this case, data association is required to complete the assignment and resolve the ambiguity.

The data association algorithm given below can be used to remove the ambiguity.

1. Examine the tentative assignments produced by the gating step.
2. For each trajectory that is tentatively assigned a single unique measured value, assign the measured value to the trajectory. Discard from further examination the trajectory and the measured value, together with all tentative assignments involving them.
3. For each measured value that is tentatively assigned to a single trajectory, discard the tentative assignments of those measured values that are tentatively assigned to this trajectory if the values are also assigned to some other trajectories.
4. Sort the remaining tentative assignments in order of non-decreasing distance.
5. Assign the measured value given by the first tentative assignment in the list to the corresponding trajectory and discard the measured value and trajectory.
6. Repeat step (3) until the list of tentative assignments is empty.

Other Real Time Applications

The two most common real-time applications are real-time analysis and multimedia applications. These are described below.

Real Time Databases

The term real-time data base systems refers to a diverse spectrum of information systems that ranges from stock price quotation systems, to track records databases, to real-time file systems. In the table shown above, lists several examples. The perishable nature of the data maintained by the databases distinguish them from non-real time databases. Specifically, a real-time database contains data objects, called image objects, which represent real-world objects. The attributes of an image object are those of the represented real world object. As an example, an air traffic control database contains image objects which represent aircraft in the coverage area. The attributes of that kind of image object include the position and heading of the aircraft. The values of these attributes are updated periodically based on the measured values of the actual position and heading. The values of the actual position and headings are provided by the radar system. Without this update, the stored position and heading will deviate more and more from the actual position and heading. In away, the quality of stored data degrades. This is reason, real-time data are said to be perishable. In contrast, an underlying assumption of non-real-time databases (for example, a payroll database) is that in the absence of updates the data contained in them remain good (that is., the database remains in some consistent state satisfying all the data integrity constraints of the database).(Liu 19-21)

Absolute Temporal Consistency: A set of data objects is said to be absolutely (temporally) consistent if the maximum age of the objects in the set is no greater than a certain threshold.

Relative Temporal Consistency: A set of data objects is said to be relatively consistent if the maximum difference in ages of the objects in the set is no greater than the relative consistency threshold used by the application.

Multimedia Applications

Multimedia is the most frequently encountered real-time applications. A multimedia application may process, store, transmit, and display any number of video streams, audio streams, images, graphics, and text. A video stream is a sequence of data frames which encodes a video. An audio stream encodes a voice, sound, or music. Without compression, the storage space and transmission bandwidth required by a video are enormous.

(For example, consider a small 100×100-pixel, 30-frames/second color video. The sample values of a luminance and two chrominance signal components gives the intensity and color of each pixel, respectively, at the location of the pixel. If they are not compressed, the video requires a transmission bandwidth of 2.7 Mbits per second when the value of each component at each pixel is encoded with 3 bits.) Therefore, a video stream and the associated audio stream, is invariably compressed as soon as it is captured. (Liu 22)

References

Liu, Jane W. S. Real Time Systems. Integre Technical Publishing Co., Inc, January 10, 2000. Print.