DZone
Thanks for visiting DZone today,
Edit Profile
  • Manage Email Subscriptions
  • How to Post to DZone
  • Article Submission Guidelines
Sign Out View Profile
  • Post an Article
  • Manage My Drafts
Over 2 million developers have joined DZone.
Log In / Join
Please enter at least three characters to search
Refcards Trend Reports
Events Video Library
Refcards
Trend Reports

Events

View Events Video Library

Zones

Culture and Methodologies Agile Career Development Methodologies Team Management
Data Engineering AI/ML Big Data Data Databases IoT
Software Design and Architecture Cloud Architecture Containers Integration Microservices Performance Security
Coding Frameworks Java JavaScript Languages Tools
Testing, Deployment, and Maintenance Deployment DevOps and CI/CD Maintenance Monitoring and Observability Testing, Tools, and Frameworks
Culture and Methodologies
Agile Career Development Methodologies Team Management
Data Engineering
AI/ML Big Data Data Databases IoT
Software Design and Architecture
Cloud Architecture Containers Integration Microservices Performance Security
Coding
Frameworks Java JavaScript Languages Tools
Testing, Deployment, and Maintenance
Deployment DevOps and CI/CD Maintenance Monitoring and Observability Testing, Tools, and Frameworks

Modernize your data layer. Learn how to design cloud-native database architectures to meet the evolving demands of AI and GenAI workkloads.

Secure your stack and shape the future! Help dev teams across the globe navigate their software supply chain security challenges.

Releasing software shouldn't be stressful or risky. Learn how to leverage progressive delivery techniques to ensure safer deployments.

Avoid machine learning mistakes and boost model performance! Discover key ML patterns, anti-patterns, data strategies, and more.

Related

  • The LLM Advantage: Smarter Time Series Predictions With Less Effort
  • Optimizing Prometheus Queries With PromQL
  • Utilizing AI and Database Technologies to Stimulate Innovation
  • How to Enable Azure Databricks Lakehouse Monitoring Through Scripts

Trending

  • Testing SingleStore's MCP Server
  • Integrating Security as Code: A Necessity for DevSecOps
  • Unlocking the Potential of Apache Iceberg: A Comprehensive Analysis
  • Beyond ChatGPT, AI Reasoning 2.0: Engineering AI Models With Human-Like Reasoning
  1. DZone
  2. Data Engineering
  3. Databases
  4. Time Series Analysis vs. DSP Terminology

Time Series Analysis vs. DSP Terminology

Digital signal processing and time series analysis are very similar — but the terminology that they use is very different. This article is here to clarify the confusion.

By 
John Cook user avatar
John Cook
·
Oct. 26, 17 · Opinion
Likes (6)
Comment
Save
Tweet
Share
4.8K Views

Join the DZone community and get the full member experience.

Join For Free

Time series analysis and digital signal processing are closely related. Unfortunately, the two fields use different terms to refer to the same things.

Suppose you have a sequence of inputs x[n] and a sequence of outputs y[n] for integers n.

Moving Average/FIR

If each output depends on a linear combination of a finite number of previous inputs:

Image title

...then time series analysis would call this a moving average (MA) model of order q, provided b0 = 1. Note that this might not really be an average, i.e. the bs are not necessarily positive and don't necessarily sum to 1.

Digital signal processing would call this a finite impulse response (FIR) filter of order q.

Autoregressive/IIR

If each output depends on a linear combination of a finite number of previous outputs:

Image title

...then time series analysis would call this an autoregressive (AR) model of order p.

Digital signal processing would call this an infinite impulse response (IIR) filter of order p.

Sometimes, you'll see the opposite sign convention on the as.

ARMA/IIR

If each output depends on a linear combination of a finite number of previous inputs and outputs:

Image title

...then time series analysis would call this an autoregressive moving average (ARMA) model of order (p, q), i.e. p AR terms and q MA terms.

Digital signal processing would call this an infinite impulse response (IIR) filter with q feedforward coefficients and p feedback coefficients. Also, as above, you may see the opposite sign convention on the as.

ARMA Notation

Box and Jenkins use as for input and zs for output. We'll stick with xs and ys to make the comparison to DSP easier.

Using the backward shift operator B that takes a sample at n to the sample at n-1, the ARMA system can be written as:

Image title

...where φ and θ are polynomials, and:

Image title

System Function Notation

In DSP, filters are described by their system function, the z-transform of the impulse response. In this notation (as in Oppenheim and Shafer, for example), we have:

Related

  • DSP and time series consulting
Time series

Published at DZone with permission of John Cook, DZone MVB. See the original article here.

Opinions expressed by DZone contributors are their own.

Related

  • The LLM Advantage: Smarter Time Series Predictions With Less Effort
  • Optimizing Prometheus Queries With PromQL
  • Utilizing AI and Database Technologies to Stimulate Innovation
  • How to Enable Azure Databricks Lakehouse Monitoring Through Scripts

Partner Resources

×

Comments
Oops! Something Went Wrong

The likes didn't load as expected. Please refresh the page and try again.

ABOUT US

  • About DZone
  • Support and feedback
  • Community research
  • Sitemap

ADVERTISE

  • Advertise with DZone

CONTRIBUTE ON DZONE

  • Article Submission Guidelines
  • Become a Contributor
  • Core Program
  • Visit the Writers' Zone

LEGAL

  • Terms of Service
  • Privacy Policy

CONTACT US

  • 3343 Perimeter Hill Drive
  • Suite 100
  • Nashville, TN 37211
  • support@dzone.com

Let's be friends:

Likes
There are no likes...yet! 👀
Be the first to like this post!
It looks like you're not logged in.
Sign in to see who liked this post!