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Prepared by: Hind J. Zourob 220033212 Heba M. Matter 220012336 Supervisor :

Prepared by: Hind J. Zourob 220033212 Heba M. Matter 220012336 Supervisor : Dr. Hatem El-Aydi. Faculty Of Engineering Communications & Control Engineering Department. Fixed point vs. Floating point. Digital Signal Processing. Introduction. Fixed point processors.

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Prepared by: Hind J. Zourob 220033212 Heba M. Matter 220012336 Supervisor :

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  1. Prepared by: Hind J. Zourob 220033212 Heba M. Matter 220012336 Supervisor: Dr. Hatem El-Aydi Faculty Of Engineering Communications & Control Engineering Department Fixed point vs. Floating point Digital Signal Processing

  2. Introduction. • Fixed point processors. • Q Format. • Floating point processors. • Overflow and scaling. • Scaling. • Comparison. • Conclusion. Outlines Digital Signal Processing -

  3. Digital Signal Processing can be divided into two categories, • Fixed point • Floating point. • Refer to the format used to store and manipulate numbers within the devices. Introduction Digital Signal Processing -

  4. Represents each number with a minimum of 16 bits. • Numbers are represented and manipulated in integer format. • There are four common ways that these 2^16=65,536 possible bit patterns can represent a number: • unsigned integer • signed integer • unsigned fraction notation • signed fraction format Fixed point processors Digital Signal Processing -

  5. There is simply no need for the floating-point processing in mobile TVs. • Indeed, floating point computations would produce a more precise DCT, Unfortunately, the DCTs in video codec are designed to be performed on a fixed point processor and are bit-exact. Fixed point processors usages Digital Signal Processing -

  6. In a 16-bit system, it is not possible to represent numbers larger than 32767 and smaller than –32768. • To cope with this limitation, numbers are often normalized between -1,1. • This achieved by moving the implied binary point. Number representations Q Format (Fractional Representation) Digital Signal Processing -

  7. ExamplesExample (1)Consider two Q15 format numbers are multipliedwhat the result and how will it be stored in 16 bit memory? Digital Signal Processing -

  8. Example (2)Any multiplication or addition resulting in a number larger than 7 or smaller than –8 will cause overflow.When 6 is multiplied by 2, we get 12.The result will be wrapped around the circle to 1100, which is –4.How to solve this problem? The third example will answer Digital Signal Processing -

  9. Example (3) Digital Signal Processing -

  10. It should be realized that some precision is lost. • As a result of discarding the smaller fractional bits. • To solve this problem, the scaling approach will be used (discussed later) But…. Digital Signal Processing -

  11. Use a minimum of 32 bits to store each value. • The represented numbers are not uniformly spaced. • Composed of a mantissa and exponent • Floating point processor can also support integer representation and calculations. • There are two floating-point data representations on the C67x processor: • single precision (SP) • and double precision(DP). Floating point Number representation Digital Signal Processing -

  12. C67x floating-point data representation. Single precision and double precision C67x double precision floating-point representation Digital Signal Processing -

  13. All steps needed to perform floating-point arithmetic are done by the floating-point hardware. • It is inefficient to perform floating-point arithmetic on fixed-point processors ,Since all the operations involved, must be done in software. Floating point processors Digital Signal Processing -

  14. In military radar, the floating point processor is frequently used because its performance is essential. • Floating point processing is good for doing large FFTs so we can implement the FIR in frequency domain. • Appropriate in systems where gain coefficients are changing with time or coefficients have large dynamic ranges . Floating point processors usages Digital Signal Processing -

  15. When multiplying two Q15 numbers, which are in the range of –1 and 1the product will be in the same range. • However, when two Q15 numbers are added, the sum may fall outside this range, leading to an overflow. • Overflows can cause major problems by generating erroneous results. • The simplest correction method for overflow is scaling. Overflow and scaling Digital Signal Processing -

  16. The idea of scaling is to scale down the system input before performing any processing then to scale up the resulting output to the original size. • Scaling can be applied to most filtering and transform operations. • An easy way to achieve scaling is by shifting. • Since a right shift of 1 is equivalent to a division by 2, we can scale the input repeatedly by 0.5 until all overflows disappear. • The output can then be rescaled back to the total scaling amount. Scaling Digital Signal Processing -

  17. Comparison Digital Signal Processing -

  18. DSP processors are designed as fixed point and floating point. • Fixed-point • Partition a binary word into integer and fractional • Radix point is in a fixed position • Floating-point • Large dynamic range • Composed of a mantissa and exponent • Scaling solves the problem of overflow. • Comparison between fixed point and floating point Conclusion Digital Signal Processing -

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