We present the first analysis of Cepheid stars observed by the TESS space mission in Sectors 1–5. Our sample consists of 25 pulsators: ten fundamental mode, three overtone and two double-mode classical Cepheids, plus three type II and seven anomalous Cepheids. The targets were chosen from fields with different stellar densities, both from the Galactic field and from the Magellanic System. Three targets have 2 minutes cadence light curves available by the TESS Science Processing Operations Center: for the rest, we prepared custom light curves from the full-frame images with our own differential photometric FITSH pipeline. Our main goal was to explore the potential and the limitations of TESS concerning the various subtypes of Cepheids. We detected many low-amplitude features: weak modulation, period jitter, and timing variations due to light-time effect. We also report signs of nonradial modes and the first discovery of such a mode in an anomalous Cepheid, the overtone star XZ Cet, which we then confirmed with ground-based multicolor photometric measurements. We prepared a custom photometric solution to minimize saturation effects in the bright fundamental-mode classical Cepheid, β Dor with the lightkurve software, and we revealed strong evidence of cycle-to-cycle variations in the star. In several cases, however, fluctuations in the pulsation could not be distinguished from instrumental effects, such as contamination from nearby sources, which also varies between sectors. Finally, we discuss how precise light-curve shapes will be crucial not only for classification purposes but also to determine physical properties of these stars.

我们对 TESS 空间任务在 1-5 区观测到的造父变星进行了首次分析。我们的样本由 25 个波轮组成：十个基本模式、三个泛音和两个双模式经典造父变星，加上三个 II 型和七个异常造父变星。目标是从具有不同恒星密度的场中选择的，包括银河场和麦哲伦系统。TESS 科学处理操作中心提供三个目标的 2 分钟节奏光曲线：对于其余的，我们使用我们自己的差分光度测量 FITSH 管道从全帧图像准备自定义光曲线。我们的主要目标是探索 TESS 在造父变种的各种亚型方面的潜力和局限性。我们检测到许多低幅度特征：弱调制、周期抖动、和由于光时效应引起的时间变化。我们还报告了非径向模式的迹象，以及在异常造父变星——泛音星 XZ Cet 中首次发现这种模式，然后我们通过地面多色光度测量证实了这一点。我们准备了一个定制的光度学解决方案，以最大限度地减少明亮基模经典造父变星中的饱和效应，β Dor 与lightkurve软件，我们揭示了恒星周期变化的有力证据。然而，在一些情况下，脉动的波动无法与仪器效应区分开来，例如来自附近源的污染，这在部门之间也有所不同。最后，我们讨论精确的光曲线形状不仅对分类目的而且对确定这些恒星的物理特性至关重要。