Reconstruction of a Signal Sampled Slower than the Usual Nyquist Rate Using Complex Sampling

Yıl 2025, Cilt: 9 Sayı: 1, 108 - 117, 31.07.2025

Hüseyin Canbolat

Öz

In this paper, a modified sampling rate, which is smaller than the usual Nyquist rate, is determined for bandlimited signals using a method like single side band (SSB-like). SSB-like method is characterized using the base signal of single side band Amplitude Modulation (SSB-AM) instead of the actual AM signal. The sampling should be performed on the base SSB signal, which is a complex valued signal. That is, SSB-like sampling is performed on a complex valued signal with a corresponding Nyquist frequency which is half of the actual required sampling frequency. Also, a theoretical sampling method is proposed as a theorem that results in sampled values based on the mathematical properties of transformations. The proposed complex sampling method is novel in the context of sampling and valid for any band-limited real valued signal. The application of the method to real physical cases and a block diagram for complex sampling is under study.

Anahtar Kelimeler

complex sampling , amplitude modulation (AM) , SSB-AM , Nyquist rate , signal reconstruction

Nyquist Frekansından daha Yavaş Örneklenmiş bir Sinyalin Kompleks Örenklemeyle Tekrar Oluşturulması

Öz

In this paper, a modified sampling rate, which is smaller than the usual Nyquist rate, is determined for bandlimited signals using a method like single side band (SSB-like). SSB-like method is characterized using the base signal of single side band Amplitude Modulation (SSB-AM) instead of the actual AM signal. The sampling should be performed on the base SSB signal, which is a complex valued signal. That is, SSB-like sampling is performed on a complex valued signal with a corresponding Nyquist frequency which is half of the actual required sampling frequency. Also, a theoretical sampling method is proposed as a theorem that results in sampled values based on the mathematical properties of transformations. The proposed complex sampling method is novel in the context of sampling and valid for any band-limited real valued signal. The application of the method to real physical cases and a block diagram for complex sampling is under study.

Anahtar Kelimeler

Kompleks örnekleme , genlik modülasyonu (AM) , SSB-AM , Nyquist frekansı , sinyal geri oluşturma

Kaynakça

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