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$$\min_t \quad\operatorname{Re} \sum\limits_{i = 1}^N {\left( {{e^{ - j2\pi {f_i}t}}{r_i}} \right)}, $$where $\operatorname{Re}$ refers to get the real part of a complex number, $\{f_i\}$ is an arithmetic progression with $i = 1,2,...,N$, ${r_i} \in \mathcal{Z}$ are with unequal modulus and angles.

$$\min_t \quad\operatorname{Re} \sum\limits_{i = 1}^N {\left( {{e^{ - j2\pi {f_i}t}}{r_i}} \right)}, $$where $\operatorname{Re}$ refers to get the real part of a complex number, $\{f_i\}$ is an arithmetic progression with $i = 1,2,...,N$, ${r_i} \in \mathcal{Z}$ are with unequal modulus and angles.

This is a question from the field of signal processing, and $j$ refers to the imaginary unit, $N=128$, $f_i=f_c+\frac{B}{N}\left(i-1-\frac{N-1}{2}\right), \text { for } i=1,2, \ldots, N$, $f_c = 3*10^{11}$, $B=3*10^{10}$.

$$\min_t \quad\quad\operatorname{Re} \sum\limits_{i = 1}^N {\left( {{e^{ - j2\pi {f_i}t}}{r_i}} \right)}, $$where $\operatorname{Re}$ refers to get the real part of a complex number, $\{f_i\}$ is an arithmetic progression with $i = 1,2,...,N$, ${r_i} \in \mathcal{Z}$ are with unequal modulus and angles.

$$\min_t \quad\operatorname{Re} \sum\limits_{i = 1}^N {\left( {{e^{ - j2\pi {f_i}t}}{r_i}} \right)}, $$where $\operatorname{Re}$ refers to get the real part of a complex number, $\{f_i\}$ is an arithmetic progression with $i = 1,2,...,N$, ${r_i} \in \mathcal{Z}$ are with unequal modulus and angles.

$$\min_t \operatorname{Re} \sum\limits_{i = 1}^N {\left( {{e^{ - j2\pi {f_i}t}}{r_i}} \right)}, $$where $\operatorname{Re}$ refers to get the real part of a complex number, $\{f_i\}$ is an arithmetic progression with $i = 1,2,...,N$, ${r_i} \in \mathcal{Z}$ are with unequal modulus and angles.

$$\min_t \quad\quad\operatorname{Re} \sum\limits_{i = 1}^N {\left( {{e^{ - j2\pi {f_i}t}}{r_i}} \right)}, $$where $\operatorname{Re}$ refers to get the real part of a complex number, $\{f_i\}$ is an arithmetic progression with $i = 1,2,...,N$, ${r_i} \in \mathcal{Z}$ are with unequal modulus and angles.