On the Arithmetic Complexity of the Bandwidth of Bandlimited Signals

02/04/2022
by   Holger Boche, et al.
0

The bandwidth of a signal is an important physical property that is of relevance in many signal- and information-theoretic applications. In this paper we study questions related to the computability of the bandwidth of computable bandlimited signals. To this end we employ the concept of Turing computability, which exactly describes what is theoretically feasible and can be computed on a digital computer. Recently, it has been shown that there exist computable bandlimited signals with finite energy, the actual bandwidth of which is not a computable number, and hence cannot be computed on a digital computer. In this work, we consider the most general class of band-limited signals, together with different computable representations thereof. Among other things, our analysis includes a characterization of the arithmetic complexity of the bandwidth of such signals and yields a negative answer to the question of whether it is at least possible to compute non-trivial upper or lower bounds for the bandwidth of a bandlimited signal. Furthermore, we relate the problem of bandwidth computation to the theory of oracle machines. In particular, we consider halting and totality oracles, which belong to the most frequently investigated oracle machines in the theory of computation.

READ FULL TEXT
research
01/27/2022

Capacity of Finite State Channels with Feedback: Algorithmic and Optimization Theoretic Properties

The capacity of finite state channels (FSCs) with feedback has been show...
research
12/27/2017

On low for speed oracles

Relativizing computations of Turing machines to an oracle is a central c...
research
01/30/2020

Computability of the Zero-Error capacity with Kolmogorov Oracle

The zero-error capacity of a discrete classical channel was first define...
research
08/30/2020

Shannon Meets Turing: Non-Computability and Non-Approximability of the Finite State Channel Capacity

The capacity of finite state channels (FSCs) has been established as the...
research
05/04/2023

Algorithmic Computability of the Capacity of Gaussian Channels with Colored Noise

Designing capacity achieving coding schemes for the band-limited additiv...
research
02/24/2022

On the relevance of bandwidth extension for speaker identification

In this paper we discuss the relevance of bandwidth extension for speake...
research
07/05/2017

The Complexity of Human Computation: A Concrete Model with an Application to Passwords

What can humans compute in their heads? We are thinking of a variety of ...

Please sign up or login with your details

Forgot password? Click here to reset