Note: This document applies to Intel MKL 10.0 or later and Intel IPP 6.0 or later.

Objective

The purpose of this document is to help developers determine which FFT, Intel MKL or Intel IPP, is best for their application.

Overview

Fourier transforms are used in signal processing, image processing, physics, statistics, finance, cryptography, and many other areas. The Discrete Fourier transform (DFT) mathematical operation converts a signal from the time domain to the frequency domain and back.

DFT processing time can dominate a software application. Using a fast algorithm, Fast Fourier transform (FFT), reduces the number of arithmetic operations from O(N²) to O(N log₂ N) operations. Intel MKL and Intel IPP are highly optimized for Intel architecture-based multi-core processors using the latest instruction sets, parallelism, and algorithms.

Read further to decide which FFT is best for your application.

Below is a brief summary of the Intel MKL and Intel IPP libraries. For more details on these products, visit the Intel MKL web site and the Intel IPP web site.

Table 1: Comparison of Intel MKL and Intel IPP Functionality

Intel MKL and Intel IPP Fourier Transform Features

The Fourier Transforms provided by MKL and IPP are respectively targeted for the types of applications targeted by MKL (engineering and scientific) and IPP (media and communications).  In the table below, we highlight specifics of the MKL and IPP Fourier Transforms that will help you decide which may be best for your application.

Table 2: Comparison of Intel MKL and Intel IPP DFT Features

Data Types and Formats

The Intel MKL and Intel IPP Fourier transform functions support a variety of data types and formats for storing signal values. Mixed types interfaces are also supported. Please see the product documentation for details.

Table 3: Comparison of Intel MKL and Intel IPP Data Types and Formats

Formats Legend
CCE - stores the values of the first half of the output complex conjugate-even signal
CCS - same format as CCE format for 1D, is slightly different for multi-dimensional real transforms
For 2D transforms. CCS, Pack, Perm are not supported for 3D and higher rank
Pack - compact representation of a complex conjugate-symmetric sequence
Perm - same as Pack format for odd lengths, arbitrary permutation of the Pack format for even lengths
RCPack2D - exploits the complex conjugate symmetry of the transformed data to store only half of the resulting Fourier coefficients


Performance

The Intel MKL and Intel IPP are optimized for current and future Intel® processors, and are specifically tuned for two different usage areas:

• Intel MKL is suitable for large problem sizes typical to FORTRAN and C/C++ high-performance computing software such as engineering, scientific, and financial applications.
• Intel IPP is specifically designed for smaller problem sizes including those used in multimedia, data processing, communications, and embedded C/C++ applications.

Choosing the Best FFT for Your Application

Before making a decision, developers must understand the specific requirements and constraints of the application. Developers should consider these questions:

• What are the performance requirements for the application? How is performance measured and what is the measurement criteria? Is a specific benchmark being used? What are the known performance bottlenecks?
• What type of application is being developed? What are the main operations being performed and on what kind of data?
• What API is currently being used in the application for transforms? What programming language(s) is the application code written in?
• Does the FFT output data need to be scaled (normalized)? What type of scaling is required?
• What kind of input and output data does the transform process? What are the valid and invalid values? What type of precision is required?

Summary

Intel MKL and Intel IPP both provide optimized Fourier Transform functions. For more detailed information on the FFT APIs, parameters and formats, please refer to the following documents:

• Intel MKL Reference Manual (Chapter 11)
• Intel IPP Reference Manual Volume 1: Signal Processing (1D) (Chapter 7)
• Intel IPP Reference Manual Volume 2: Image Processing (2D) (Chapter 10)

 30-day evaluation packages are available for free download.

Other Resources

• Intel MKL Web Site
• Intel IPP Web Site

Notes:
*   - Actually less than 2^32. Maximum int is 2^31-1, but allowed maximum size is even smaller, ~2^29.
** - Both libraries support arbitrary radix in optimized manner, that is O(N log N), but these specific radixes are better optimized than others. MKL 10.1u1 and on include radix 11 too.