1 / 18

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.

cicely
Télécharger la présentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 -

More Related