In Chapter 5 we showed that the thermal noise of a receiver sets a lower limit on the signal detectable at the receiver input. The upper limit to the maximum signal a receiver can handle is set by the distortion, arisen from nonlinearity present in the active circuits making up the receiver. However, handling a desired large input is generally not an issue as it is typically managed by the proper gain control in the receiver. On the other hand, we will show in this chapter that the distortion has a far more detrimental impact on the receiver, when subject to large unwanted signals, known as blockers. Similar to noise, the blockers will also set a lower limit on the detectable signal.

In cases of international or cross-cultural research we need to take extra care at every stage of the process, and this chapter looks at various aspects of this. Research involving unfamiliar environmental and cultural differences may complicate the understanding of the research problem, and researchers often fail to anticipate the impact of local cultures on the question asked. Consideration also needs to be given to the scope and limits of the problem. In some cultures, a broader scope is necessary to cover the necessary variables. Comparability of data is the main issue in international/cross-cultural research, and it is not possible to use data gathered in one market for another market. This is due not just to the availability and reliability of data but also to the manner in which data are collected and analysed.

This chapter outlines the purpose, scope, and structure of the book and introduces the scientific, data-driven approach to analysing and solving business problems and conducting business research.

At the opposite extreme to the results of the last chapter, we now consider unbounded operators on Hilbert spaces. We define an appropriate notion of the Hilbert adjoint in this setting and show that for unbounded self-adjoint operators, we can develop a good spectral theory.

We recall the definition of a metric sapce, along with definitions of convergence, continuity, separability, and compactness. The treatment is intentionally brisk, but proofs are included.

We define the resolvent and spectrum of a bounded linear operator and discuss the relationship between the spectrum and the ‘point spectrum’, which is the set of all eigenvalues. We prove some basic properties of the spectrum and the Spectral Mapping Theorem for polynomials.

It is one of the major results of finite-dimensional linear algebra that all the eigenvalues of real symmetric matrices are real and that the eigenvectors of distinct eigenvalues are orthogonal. In this chapter we prove similar results for compact self-adjoint operators on infinite-dimensional HIlbert space: we show that the spectrum consists entirely of real eigenvalues (except perhaps zero), that the multiplicity of every non-zero eigenvalue is finite, and that the eigenvectors form an orthonormal basis for H. The last fact follows from the Hilbert-Schmidt Theorem, which allows us to write such operators in terms of their eigenvalues and eigenvectors.

In business studies most researchers need to collect some primary data to answer their research question. This entails deciding what kind of data collection method to use, which depends upon an overall judgement on which type of data is needed for a particular research problem. One important aspect is to identify the scope of the study and unit of analysis and what type of analysis is needed. After looking briefly at the chief differences between quantitative and qualitative approaches, the chapter looks at different qualitative methods and when to use them.

Qualitative research imposes specific analytical challenges. This chapter addresses important characteristics of qualitative research and qualitative data. Strategies and procedures to handle the analytical challenges are also dealt with, as well as validity and reliability issues in qualitative research.

This chapter deals with some conceptual (theoretical) foundations of research. Practical business research is often thought of as collecting data from various statistical publications, constructing questionnaires, and analysing data by using computers. Research, however, also comprises a variety of important, non-empirical tasks, such as finding/‘constructing’ a precise problem, and developing perspectives or models to represent the problem under scrutiny. In fact, such aspects of research are often the most crucial and skill demanding. The quality of the work done at the conceptual (theoretical) level largely determines the quality of the final empirical research. This is also the case in practical business research. Important topics focused on in this chapter are the research process and the role of concepts and theory.

The most commonly used technique for the analysis of quantitative data in business research is multiple regression analysis. This is a powerful technique for understanding the relationships between variables, which variables have the most impact, and for prediction. In this chapter, we consider how to specify regression models, how to estimate the models, and how to use the estimated models to undertake some simple hypothesis tests. We emphasize that the researcher has to exercise his/her judgement in deciding not only the specification of the initial model but also in how to adapt and interpret the model in response to the various statistical tests.

In this chapter we study the challenging problem of delivering power to antenna efficiently. The linear amplifier topologies that we have discussed thus far are fundamentally incapable of achieving high efficiency. Considering the high demand for improving battery life, this shortcoming becomes very critical when delivering hundreds of mW or several watts of power into the antenna. This issue is exacerbated in most modern radios that employ complex modulation schemes to improve the throughput without raising the bandwidth. As we discussed in Chapter 6, such systems demand more linearity on the power amplifier, and hence achieving a respectable efficiency becomes more of a challenge.