Abstract—Integration of multimodal measurement signals is necessary for extending the experiment scope, for avoiding accidental data or synchronization loss or for building authorization-dependent data supplement. Instead of signal modulation or packet transmission widely used in such cases, we propose using of efficient watermarking technique based on the bandgap occasionally appearing between the instantaneous bandwidth of the signal and the Nyquist frequency. Usage of the method requires anticipating studies of the carrier (i.e. main signal) to determine band limits and a confident detection method of its components. Resulting statistics lead to a signal- specific standardized instantaneous bandwidth function. The method starts with detection of signal components, estimating the expected local bandwidth and measuring of noise properties in the bandgap. The supplementary data are tailored and packetized as so mimic the noise, therefore are not interfering with the carrier message and not conspicuous for an unauthorized reader. Finally an individual description of each packet is made and encoded with optional encryption. As long as the total data streams volume does not excess the channel throughput, the proposed integrating uses the carrier's original transmission channel (with no carrier delay) and data storage structures. The research was showcased by three applications of watermarking the ECG signal for its best methods for automatic components detection, best knowledge on physiological backgrounds and best documented annotated databases of reference records. Nevertheless, the results of our research will be applicable for any digital measurement series (signals) recorded in biology and industry in which the instantaneous bandwidth could be estimated. Keywords— time-frequency steganography, variable bandwidth, multimodal measurements, biosignal watermarking. I. INTRODUCTION AST development of data interpretation methods requires constant evolution of measurement infrastructure. This is partially faced by development of new sensors and sensing methods, but yet rarely supported by recording hardware and software. Additionally, backward compatibility of digital records is usually in question when adding supplementary structures to the storage format. The concept of bandgap stems directly from the sampling theorem which requires that a sequential measurement (e.g. of This scientific work is supported by the AGH University of Science and Technology in year 2018 as a research project No. 11.11.120.612. Piotr Augustyniak is with the AGH-University of Science and Technology 30, Mickiewicz Ave, 30-059 Krakow, Poland; (e-mail: august@agh.edu.pl). . the voltage) was performed at least at twice of the maximal frequency of signal components (also called the Nyquist frequency), without additional assumption on their occurrence in time. Consequently, the bandwidth of discrete signal representation is being fully engaged in short time intervals only, while beyond these intervals it is overestimated and its redundant part does not carry components originated from the signal source. A bandgap occasionally appears between the variable instantaneous bandwidth of the signal the constant Nyquist frequency. It represents the noise component only. Time intervals with overestimated sampling and thus with the bandgap can be identified and localized by automatic detection of signal components provided they have a specific, a priori known limits of bandwidth. The existence of bandgap may be employed for accurate noise estimation [1], bit-accurate compression [2] or watermarking with supplementary data [3]. The latter case is presented in this paper. The concept of bandgap is also hidden in image processing and used for compressed storage of images with smooth or texture-like regions detected. These parts are then efficiently represented with various techniques (e.g. multiresolution decomposition [4], [5]) without perceptible loss of quality. Digital images are well explored towards supplementary data embedment including steganography, secret sharing (e.g. [6], [7], [8], [9]) and encapsulating of other information such as in DICOM standard for medical images [10], [11], [12]. However, images due to their rigid structure (resolution, definition and frame rate) can be considered as packets and will not be discussed here. II. METHODS A. General Case A constant-bandwidth analog signal fills the throughput of transmission channel completely when the sampling frequency exactly matches the double of its bandwidth. This assumption is impractical for non-stationary signals and technical measuring systems overestimate the necessary throughput in order to avoid the aliasing. When seamless digital transmission is used, the constant-throughput channel is continuously available. Otherwise the signal is embedded in data packets and travel to the destination accordingly to a specific routing protocol. This allows for more economic usage of the channel, however the price for occasional excesses of channel throughput or transmission breaks is possible data delay. Time-Frequency Integration of Variable-Bandwidth Signals and Supplementary Data Packets Piotr Augustyniak F INTERNATIONAL JOURNAL OF BIOLOGY AND BIOMEDICAL ENGINEERING Volume 12, 2018 ISSN: 1998-4510 114